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  • American Institute of Physics (AIP)  (26,481)
  • Canadian Science Publishing
  • 2000-2004  (29,501)
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  • 1
    Electronic Resource
    Electronic Resource
    Noncanonical quantization of gravity. II. Constraints and the physical Hilbert space (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4440-4465 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The program of quantizing the gravitational field with the help of affine field variables is continued. For completeness, a review of the selection criteria that singles out the affine fields, the alternative treatment of constraints, and the choice of the initial (before imposition of the constraints) ultralocal representation of the field operators is initially presented. As analogous examples demonstrate, the introduction and enforcement of the gravitational constraints will cause sufficient changes in the operator representations so that all vestiges of the initial ultralocal field operator representation disappear. To achieve this introduction and enforcement of the constraints, a well characterized phase space functional integral representation for the reproducing kernel of a suitably regularized physical Hilbert space is developed and extensively analyzed. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1385375
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  • 2
    Electronic Resource
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    False vacuum decay: Effective one-loop action for pair creation of domain walls (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3292-3298 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An effective one-loop action built from the soliton field itself for the two-dimensional (2D) problem of soliton pair creation is proposed. The action consists of the usual mass term and a kinetic term in which the simple derivative of the soliton field is replaced by a covariant derivative. In this effective action the soliton charge is treated no longer as a topological charge but as a Noether charge. Using this effective one-loop action, the soliton–antisoliton pair production rate Γ/L=A exp[−S0] is calculated and one recovers Stone's exponential factor S0 and the prefactor A of Kiselev, Selivanov, and Voloshin. The results are also valid straightforwardly to the problem of pair creation rate of domain walls in dimensions D≥3. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1380442
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  • 3
    Electronic Resource
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    The Bargmann transform and canonical transformations (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2249-2283 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper concerns a relationship between the kernel of the Bargmann transform and the corresponding canonical transformation. We study this fact for a Bargmann transform introduced by Thomas and Wassell [J. Math. Phys. 36, 5480–5505 (1995)]—when the configuration space is the two-sphere S2 and for a Bargmann transform that we introduce for the three-sphere S3. It is shown that the kernel of the Bargmann transform is a power series in a function which is a generating function of the corresponding canonical transformation (a classical analog of the Bargmann transform). We show in each case that our canonical transformation is a composition of two other canonical transformations involving the complex null quadric in C3 or C4. We also describe quantizations of those two other canonical transformations by dealing with spaces of holomorphic functions on the aforementioned null quadrics. Some of these quantizations have been studied by Bargmann and Todorov [J. Math. Phys. 18, 1141–1148 (1977)] and the other quantizations are related to the work of Guillemin [Integ. Eq. Operator Theory 7, 145–205 (1984)]. Since suitable infinite linear combinations of powers of the generating functions are coherent states for L2(S2) or L2(S3), we show finally that the studied Bargmann transforms are actually coherent states transforms. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1468254
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  • 4
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    Finite dimensional Hamiltonian formalism for gauge and quantum field theories (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2306-2347 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We discuss in this article the canonical structure of classical field theory in finite dimensions within the pataplectic Hamiltonian formulation, where we put forward the role of Legendre correspondence. We define the generalized Poisson p-brackets which are the analogs of the Poisson bracket on forms. We formulate the equations of motion of forms in terms of p-brackets. As illustration of our formalism we present three examples: the interacting scalar fields, conformal string theory and the electromagnetic field. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1467710
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  • 5
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    Quantizing Yang–Mills theory on a two-point space (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2348-2354 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We perform the Batalin–Vilkovisky quantization of Yang–Mills theory on a two-point space, discussing the formulation of Connes–Lott as well as Connes' real spectral triple approach. Despite the model's apparent simplicity the gauge structure reveals infinite reducibility and the gauge fixing is afflicted with the Gribov problem. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1467096
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  • 6
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    Self-dual Chern–Simons vortices on Riemann surfaces (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2355-2362 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study self-dual multivortex solutions of Chern–Simons Higgs theory in a background curved space–time. The existence and decaying property of a solution are demonstrated.© 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1471365
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  • 7
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    Local existence proofs for the boundary value problem for static spherically symmetric Einstein–Yang–Mills fields with compact gauge groups (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2363-2393 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We prove local existence and uniqueness of static spherically symmetric solutions of the Einstein–Yang–Mills (EYM) equations for an arbitrary compact semisimple gauge group in the so-called regular case. By this we mean the equations obtained when the rotation group acts on the principal bundle on which the Yang–Mills connection takes its values in a particularly simple way (the only one ever considered in the literature). The boundary value problem that results for possible asymptotically flat soliton or black hole solutions is very singular and just establishing that local power series solutions exist at the center and asymptotic solutions at infinity amounts to a nontrivial algebraic problem. We discuss the possible field equations obtained for different group actions and solve the algebraic problem on how the local solutions depend on initial data at the center and at infinity. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1463216
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  • 8
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    Lax–Phillips scattering theory of a relativistic quantum field theoretical Lee–Friedrichs model and Lee–Oehme–Yang–Wu phenomenology (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2394-2422 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The scattering theory of Lax and Phillips, originally developed for classical wave equations, has recently been extended to the description of the evolution of resonant states in the framework of quantum theory. The resulting evolution law of the unstable system is that of a semigroup, and the resonant state is a well-defined function in the Lax–Phillips Hilbert space. In this paper we apply this theory to a relativistically covariant quantum field theoretical form of the two (or more) channel relativistic quantum field theoretical form of the Lee model. We show that this theory provides a rigorous underlying basis for the Lee–Oehme–Yang–Wu construction. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1461426
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  • 9
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    Global prescribed mean curvature foliations in cosmological space–times. I (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2439-2465 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This work investigates some global questions about cosmological space–times with two-dimensional spherical, plane, and hyperbolic symmetry containing "well-behaved" matter. The result is that these space–times admit a global foliation by prescribed mean curvature surfaces, which extends at least toward a crushing singularity. The time function of the foliation is geometrically defined and unique up to the choice of an initial Cauchy surface. This work generalizes a similar analysis on constant mean curvature foliations and avoids the topological obstructions arising from the existence problem. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1466882
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  • 10
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    On higher-dimensional dynamics (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2423-2438 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Technical results are presented on motion in N(〉4)D manifolds to clarify the physics of brane theory, Kaluza–Klein theory, induced-matter theory, and string theory. The so-called canonical or warp metric in five dimensions (5D) effectively converts the manifold from a coordinate space to a momentum space, resulting in a new force (per unit mass) parallel to the four-dimensional (4D) velocity. The form of this extra force is actually independent of the form of the metric, but for an unbound particle is tiny because it is set by the energy density of the vacuum or cosmological constant. It can be related to a small change in the rest mass of a particle, and can be evaluated in two convenient gauges relevant to gravitational and quantum systems. In the quantum gauge, the extra force leads to Heisenberg's relation between increments in the position and momenta. If the 4D action is quantized then so is the higher-dimensional part, implying that particle mass is quantized, though only at a level of 10−65 g or less, which is unobservably small. It is noted that massive particles which move on timeline paths in 4D can move on null paths in 5D. This agrees with the view from inflationary quantum field theory, that particles acquire mass dynamically in 4D but are intrinsically massless. A general prescription for dynamics is outlined, wherein particles move on null paths in an N(〉4)D manifold which may be flat, but have masses set by an embedded 4D manifold which is curved. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1462418
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  • 11
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    Global prescribed mean curvature foliations in cosmological space–times. II (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2466-2485 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper is devoted to the investigation of global properties of prescribed mean curvature (PMC) foliations in cosmological space–times with local U(1)×U(1) symmetry and matter described by the Vlasov equation. It turns out that these space–times admit a global foliation by PMC surfaces as well, but the techniques to achieve this goal are more complex than in the cases considered in Paper I [Henkel (2002)]. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1466883
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  • 12
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    Bi-quasi-Hamiltonian systems (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2505-2517 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general notion of bi-quasi-Hamiltonian systems is introduced and is related to previous work on various special cases of such systems. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1462856
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  • 13
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    On completeness of random exponentials in the Bargmann–Fock space (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3754-3768 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study the completeness/incompleteness properties of a system of exponentials EΛ={eπλz; λ∈Λ}, viewed as elements of the Bargmann–Fock space of entire functions. We assume that the index set Λ is a realization of a random point field in C (the support of a random measure). We prove that the properties are determined by the density of the field, i.e., by the mean number of the field points per unit area. We also discuss certain implications and motivations of our results, in particular, the jumps of the integrated density of states of the Landau Hamiltonian with the random potential, equal to the sum of point scatters. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1379311
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  • 14
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    Unitary irreducible representations of a Lie algebra for matrix chain models (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3817-3838 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way. Moreover, they are the only states with a finite number of non-zero quantum numbers with respect to a certain set of maximally commuting linearly independent quantum observables. Any other state is a tensor product of a multiple meson state and a state coming from a representation of a quotient algebra that extends and generalizes the Virasoro algebra. We expect the representation theory of this quotient algebra to describe physical systems at the thermodynamic limit. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1384866
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  • 15
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    Invariant integration on classical and quantum Lie supergroups (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3871-3897 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Invariant integrals on Hopf superalgebras, in particular, the classical and quantum Lie supergroups, are studied. The uniqueness (up to scalar multiples) of a left integral is proved, and a Z2-graded version of Maschke's theorem is discussed. A construction of left integrals is developed for classical and quantum Lie supergroups. Applied to several classes of examples the construction yields the left integrals in explicit form. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1364689
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  • 16
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    Trefoil symmetry III. The full clover extension (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3947-3964 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We aim to approach a trefoil symmetry involving (Z4×Z4;q)-graded parameters, multiplets of generators of integer spin 〈2 with naive dimensions in the interval [0,1]. The resulting full clover extension involves as particular subalgebras the minimal clover extensions previously obtained. We address the introduction of further scalar, dimensionless multiplets, and central charges. They could provide connections among external and internal symmetries, perhaps after some graded symmetry breaking. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1383560
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  • 17
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    Comment on "Uncertainty principle for proper time and mass" [J. Math. Phys 40, 1237 (1999)] (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3975-3977 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Kudaka and Matsumoto derive the uncertainty relation c2ΔmΔτ(approximate)h between the proper time τ and rest mass m of a material particle by adopting for the description of the particle the Lagrangian L=M(τ(overdot)−c−1−gμνx(overdot)μx(overdot)ν)+eAμ(x)x(overdot)μ, defined on the enlarged space (xμ,τ,M), where M is an additional dynamical variable. A key step in the derivation of their uncertainty relation is the identification of the variable M with the rest mass m. Adopting the point of view of variational analysis, we show that such an identification goes against the relativistic requirement of the path dependence of proper time. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1367329
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  • 18
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    Response to "Comment on ‘Uncertainty principle for proper time and mass' " [J. Math. Phys. 42, 3975 (2001)] (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3978-3979 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1367330
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  • 19
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    Noncommutative tachyons and K-theory (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2765-2780 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We show that the relation between D-branes and noncommutative tachyons leads very naturally to the relation between D-branes and K-theory. We also discuss some relations between D-branes and K-homology, provide a noncommutative generalization of the ABS construction, and give a simple physical interpretation of Bott periodicity. In addition, a framework for constructing Neveu–Schwarz fivebranes as noncommutative solitons is proposed. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1377270
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  • 20
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    Fundamental strings in open string theory at the tachyonic vacuum (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2844-2853 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We show that the world-volume theory on a D-p-brane at the tachyonic vacuum has solitonic string solutions whose dynamics is governed by the Nambu–Goto action of a string moving in (25+1) dimensional space–time. This provides strong evidence for the conjecture that at this vacuum the full (25+1) dimensional Poincaré invariance is restored. We also use this result to argue that the open string field theory at the tachyonic vacuum must contain closed string excitations. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1377037
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  • 21
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    Strings in AdS3 and the SL(2,R) WZW model. I: The spectrum (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2929-2960 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper we study the spectrum of bosonic string theory on AdS3. We study classical solutions of the SL(2,R) WZW model, including solutions for long strings with nonzero winding number. We show that the model has a symmetry relating string configurations with different winding numbers. We then study the Hilbert space of the WZW model, including all states related by the above symmetry. This leads to a precise description of long strings. We prove a no-ghost theorem for all the representations that are involved and discuss the scattering of the long string. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1377273
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  • 22
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    Sigma model approach to string theory effective actions with tachyons (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2854-2871 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Motivated by recent discussions of actions for tachyon and vector fields related to tachyon condensation in open string theory we review and clarify some aspects of their derivation within the sigma model approach. In particular, we demonstrate that the renormalized partition function Z(T,A) of the boundary sigma model gives the effective action for massless vectors which is consistent with the string S-matrix and beta function, resolving an old problem with this suggestion in the bosonic string case at the level of the leading F2(dF)2 derivative corrections to Born–Infeld action. We give a manifestly gauge invariant definition of Z(T,A) in non-Abelian NSR open string theory and check that its derivative reproduces the tachyon beta function in a particular scheme. We also discuss the derivation of similar actions for tachyon and massless modes in closed bosonic and NSR (type 0) string theories. In the bosonic case the tachyon potential has the structure −T2e−T, but it vanishes in the NSR string case. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1376129
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  • 23
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    Finite N AdS/CFT correspondence for Abelian and non-Abelian orbifolds, and gauge coupling unification (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2915-2928 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Although the AdS/CFT correspondence is rigorous only for an infinite N→∞ stack of D3-branes, it can be fruitfully studied for finite N as a source of gauge structures and choices for chiral fermions and complex scalars which solve the hierarchy problem by a conformal fixed point. We emphasize orbifolds AdS5×S5/Γ where the resulting GFT has N=0 supersymmetry. The fact that the complex scalars are prescribed by the construction limits the possible spontaneous symmetry breaking. Both Abelian and non-Abelian Γ are illustrated by simple examples. An accurate sin2 θ in electroweak unification can be obtained, suggesting that this approach merits further study. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1374450
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  • 24
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    Brane-world Kaluza–Klein reductions and branes on the brane (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3048-3070 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We present a systematic study of a new type of consistent "brane-world Kaluza–Klein reduction," which describes fully nonlinear deformations of codimension one objects that arise as solutions of a large class of gauged supergravity theories in diverse dimensions, and whose world-volume theories are described by ungauged supergravities with-one half of the original supersymmetry. In addition, we provide oxidations of these ansätz which are in general related to sphere compactified higher dimensional string theory or M-theory. Within each class we also provide explicit solutions of brane configurations localized on the world-brane. We show that at the Cauchy horizon (in the transverse dimension of the consistently Kaluza–Klein reduced world-brane) there is a curvature singularity for any configuration with a non-null Riemann curvature or a nonvanishing Ricci scalar that lives in the world-brane. Since the massive Kaluza–Klein modes can be consistently decoupled, they cannot participate in regulating these singularities. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1377272
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  • 25
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    D=4 chiral string compactifications from intersecting branes (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3103-3126 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Intersecting Dp-branes often give rise to chiral fermions living on their intersections. We study the construction of four-dimensional chiral gauge theories by considering configurations of type II D(3+n)-branes wrapped on nontrivial n-cycles on T2n×(R2(3−n)/ZN), for n=1, 2, 3. The gauge theories on the four noncompact dimensions of the brane world-volume are generically chiral and nonsupersymmetric. We analyze consistency conditions (RR tadpole cancellation) for these models, and their relation to four-dimensional anomaly cancellation. Cancellation of U(1) gauge anomalies involves a Green–Schwarz mechanism mediated by RR partners of untwisted and/or twisted moduli. This class of models is of potential phenomenological interest, and we construct explicit examples of SU(3)×SU(2)×U(1) three-generation models. The models are nonsupersymmetric, but the string scale may be lowered close to the weak scale so that the standard hierarchy problem is avoided. We also comment on the presence of scalar tachyons and possible ways to avoid the associated instabilities. We discuss the existence of (meta)stable configurations of D-branes on 3-cycles in (T2)3, free of tachyons for certain ranges of the six-torus moduli. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1376157
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  • 26
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    Extended objects from warped compactifications of M theory (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3161-3170 
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    Notes: We study the massive spectrum of fully wrapped branes in warped M-theory compactifications, including regimes where these states are parametrically lighter than the Planck scale or string scale. We show that many such states behave classically as extended objects in the noncompact directions in the sense that their mass grows with their size as measured along the Poincare slices making up the noncompact dimensions. On the other hand, these states can be quantized in a nontrivial regime: in particular, their spectrum of excitations in a limited regime can be obtained by a warped Kaluza–Klein reduction from ten dimensions. We briefly discuss scattering processes and loop effects involving these states, and also note the possibility of an exponential growth in the number of bound states of these objects as a function of energy. © 2001 American Institute of Physics.
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    Dynamical topology change in M theory (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3171-3187 
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    Notes: We study the topology change in M theory compactifications on Calabi–Yau three-folds in the presence of G flux (the four form field strength). In particular, we discuss vacuum solutions in strongly coupled heterotic string theory in which the topology change is inevitable within a single space–time background. For rather generic choices of initial conditions, the field equations drive the Kähler moduli outside the classical moduli space of a Calabi–Yau manifold. Consistency of the solution suggests that degenerate flop curves—just as wrapped M theory fivebranes—carry magnetic charges under the four form field strength. © 2001 American Institute of Physics.
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    On the observables describing a quantum reference frame (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2477-2489 
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    Notes: A reference frame F is described by the element g of the Poincaré group P which connects F with a given fixed frame F0. If F is a quantum frame, defined by a physical object following the laws of quantum physics, the parameters of g have to be considered as quantum observables. However, these observables are not compatible and some of them, namely the coordinates of the origin of F, cannot be represented by self-adjoint operators. Both these difficulties can be overcome by considering a positive-operator-valued measure on P, covariant with respect to the left translations of the group, namely a covariance system. We develop a construction procedure for this kind of mathematical structure. The formalism is also used to discuss the quantum observables measured with respect to a quantum reference frame. © 2001 American Institute of Physics.
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    Perturbation of a lattice spectral band by a nearby resonance (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2490-2506 
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    Notes: A soluble model of weakly coupled "molecular" and "nuclear" Hamiltonians is studied in order to exhibit explicitly the mechanism leading to the enhancement of fusion probability in case of a narrow near-threshold nuclear resonance. We, further, consider molecular cells of this type being arranged in lattice structures. It is shown that if the real part of the narrow nuclear resonance lies within the molecular band generated by the intercellular interaction, an enhancement, proportional to the inverse width of the nuclear resonance, is to be expected. © 2001 American Institute of Physics.
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    Symmetry transformations in extended irreversible thermodynamics (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2531-2539 
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    Notes: In this paper we consider symmetry transformations that preserve the first law and the second law of thermodynamics, as well as the pseudo-Riemannian structure of the Legendre manifold defined in terms of the second derivative matrix of the entropy function in extended irreversible thermodynamics. © 2001 American Institute of Physics.
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    On bidirectional fifth-order nonlinear evolution equations, Lax pairs, and directionally dependent solitary waves (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2567-2589 
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    Notes: In this paper, Lax pairs are constructed for two fifth-order nonlinear evolution equations of "Boussinesq"-type which govern wave propagation in two opposite directions. One of the equations is related to the well-known Sawada–Kotera (SK) equation and, through its bilinear form, is identified with the Ramani equation. The second equation—about which very little seems to be known—may be considered a bidirectional version of the Kaup–Kupershmidt (KK) equation and is the main focus of this study. The "anomalous" solitary wave of this latter equation is derived and is found to possess the remarkable property that its profile depends on the direction of propagation. This type of directional dependence would appear to be quite unusual and, to our knowledge, has not been reported in the literature before now. By taking an appropriate undirectional (long wave) limit, it is shown that neither the Ramani, nor the bidirectional Kaup–Kupershmidt (bKK) equation can be classified as truly "Boussinesq" in character (a distinction that is made precise in the study). Recursion formulas are given for generating an infinity of conserved densities for both equations. These are used to obtain the first few conservation laws of the bKK and Ramani equations explicitly; not surprisingly, they exhibit the same lacunary behavior as their unidirectional counterparts. In conclusion, a canonical interpretation of the N-soliton solution of the bKK equation is proposed which provides a basis for constructing these anomalous solitons in a future work. © 2001 American Institute of Physics.
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    An operator valued extension of the super Korteweg–de Vries equations (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2625-2634 
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    Notes: An extension of the super Korteweg–de Vries (KdV) integrable system in terms of operator valued functions is obtained. Following the ideas of Gardner, a general algebraic approach for finding the infinitely many conserved quantities of integrable systems is presented. The approach is applied to the above described system and infinitely many conserved quantities are constructed. In a particular case they reduce to the corresponding conserved quantities of super KdV. © 2001 American Institute of Physics.
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    Pseudo-Hermiticity versus PT-symmetry. II. A complete characterization of non-Hermitian Hamiltonians with a real spectrum (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2814-2816 
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    Notes: We give a necessary and sufficient condition for the reality of the spectrum of a non-Hermitian Hamiltonian admitting a complete set of biorthonormal eigenvectors. © 2002 American Institute of Physics.
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    Compatibility and decompositions of effects (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2817-2830 
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    Notes: Compatibility relations in effect algebras and their connections with refinements of the orthogonal partitions of unity are studied. Properties of blocks as maximal sets of compatible elements are discussed. Some special kinds of effect algebras are characterized using properties of compatibility. Using refinements, an additional structure on the effect test spaces is introduced and used to a characterization of different types of effect algebras. © 2002 American Institute of Physics.
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    Casimir energy of a semi-circular infinite cylinder (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1974-1986 
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    Notes: The Casimir energy of a semi-circular cylindrical shell is calculated by making use of the zeta function technique. This shell is obtained by crossing an infinite circular cylindrical shell by a plane passing through the symmetry axes of the cylinder and by considering only half of this configuration. All the surfaces, including the cutting plane, are assumed to be perfectly conducting. The zeta functions for scalar massless fields obeying the Dirichlet and Neumann boundary conditions on the semi-circular cylinder are constructed exactly. The sum of these zeta functions gives the zeta function for the electromagnetic field in question. The relevant plane problem is considered also. In all the cases the final expressions for the corresponding Casimir energies contain the pole contributions which are the consequence of the edges or corners in the boundaries. This implies that further renormalization is needed in order for the finite physical values for vacuum energy to be obtained for given boundary conditions. © 2001 American Institute of Physics.
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    Chaotic and irreversible properties of quantum scattering systems (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2023-2054 
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    Notes: Recent results for a free particle are generalized to N-particle quantum systems. Chaotic and irreversible behavior occurs in scattering states that belong to a certain Hilbert space K2 with a preferred time direction pointing to the future. At positive times the time evolution of positive observables exhibits quantum analogs of sensitive dependence on initial conditions, topological transitivity, and existence of a dense set of periodic points. A mixture of states in K2 can be described in terms of a density operator with thermodynamical entropy that increases to its least upper bound when the time tends to infinity. © 2001 American Institute of Physics.
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    k-cosymplectic manifolds and Lagrangian field theories (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2092-2104 
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    Notes: A geometrical description of classical field theories of first order is given. The underlying k-cosymplectic structure permits to derive the corresponding field equations. © 2001 American Institute of Physics.
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    Conformally flat anisotropic spheres in general relativity (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2129-2143 
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    Notes: The condition for the vanishing of the Weyl tensor is integrated in the spherically symmetric case. Then, the resulting expression is used to find new, conformally flat, interior solutions to Einstein equations for locally anisotropic fluids. The slow evolution of these models is contrasted with the evolution of models with similar energy density or radial pressure distribution but nonvanishing Weyl tensor, thereby bringing out the different role played by the Weyl tensor, the local anisotropy of pressure, and the inhomogeneity of the energy density in the collapse of relativistic spheres. © 2001 American Institute of Physics.
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    Wave equations with point interactions in finite energy spaces (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2184-2202 
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    Notes: Given the abstract wave equation φ¨−Δαφ=0, where Δα is the Laplace operator with a point interaction of strength α, we define and study W¯α, the associated wave generator in the phase space of finite energy states. We prove the existence of the phase flow generated by W¯α, and describe its most relevant properties with a particular emphasis on the associated symplectic structure and scattering theory. © 2001 American Institute of Physics.
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    Quantum toroidal algebra Uq(sl2,tor) and R matrices (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2293-2308 
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    Notes: We show the existence of R matrices acting on the tensor product of a certain class of representations of the quantum toroidal algebra Uq(sl2,tor). In particular, the explicit expressions of R matrices acting on the tensor product of level 1 integrable highest weight representations of Uq(sl2&dbgcaret;) are obtained. Our approach is based on the work of Chari and Pressley. © 2001 American Institute of Physics.
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    Erratum: "Three flavor neutrino oscillations in matter" [J. Math. Phys. 41, 2768 (2000)] (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2345-2345 
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    The Hausdorff entropic moment problem (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2309-2314 
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    Notes: Our aim in this paper is twofold. First, to find the necessary and sufficient conditions to be satisfied by a given sequence of real numbers {ωn}n=0∞ to represent the "entropic moments" ∫[0,a][ρ(x)]ndx of an unknown non-negative, decreasing and differentiable (a.e.) density function ρ(x) with a finite interval support. These moments are called entropic moments because they are closely connected with various information entropies (Renyi, Tsallis, ...). Second, we outline an efficient method for the reconstruction of the density function from the knowledge of its first N entropic moments. © 2001 American Institute of Physics.
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    Chirality in the context of spin 〈fraction SHAPE="CASE"〉32 particles (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1599-1611 
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    Notes: In this paper we apply the chiral spinorial approach to the description of spin 〈fraction SHAPE="CASE"〉32 particles. Chiral components of rank 3 spinor fields are considered to be the dynamical variables of the theory. The free Lagrangian is built from the same principles as in the case of spin 1 and spin 2 particles: chiral symmetry at the free field level and chiral symmetry breakdown at the interaction level. We show how the chiral spinorial approach provides an unambiguous Lagrangian approach for massless spin 〈fraction SHAPE="CASE"〉32 particles. This approach provides a fairly rich set of effective Lagrangians for the interaction of spin 〈fraction SHAPE="CASE"〉32 particles. © 2001 American Institute of Physics.
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    High-frequency asymptotics for Maxwell's equations in anisotropic media Part II: Nonlinear propagation and frequency conversion (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1636-1654 
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    Notes: This paper is devoted to the derivation of the equations that govern the propagation and frequency conversion of pulses in noncentrosymmetric crystals. The method is based upon high-frequency expansions techniques for hyperbolic quasi-linear and semilinear equations. In the so-called geometric regime we recover the standard results on the frequency conversion of pulses in nonlinear crystals. In the diffractive regime we show that the anisotropy of the diffraction operator involves remarkable phenomena. In particular the phase matching angle of a divergent pulse depends on the distance between the waist and the crystal plate. Finally we detect a configuration where the beam propagation in a biaxial crystal involves the generation of spatial solitons thanks to an anomalous one-dimensional diffraction. © 2001 American Institute of Physics.
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    The braiding for representations of q-deformed affine sl2 (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2156-2166 
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    Notes: We compute the braiding for the "principal gradation" of Uq(sl2&dbgcaret;) for |q|=1 from first principles, starting from the idea of a rigid braided tensor category. It is not necessary to assume either the crossing or the unitarity condition from S-matrix theory. We demonstrate the uniqueness of the normalization of the braiding under certain analyticity assumptions, and show that its convergence is critically dependent on the number theoretic properties of the number τ in the deformation parameter q=e2πiτ. We also examine the convergence using probability, assuming a uniform distribution for q on the unit circle. © 2001 American Institute of Physics.
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    Nonintegrability of Bianchi VIII Hamiltonian system (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1728-1743 
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    Notes: In this paper we study the Bianchi VIII cosmological dynamical system. Our aim is to show that this system is nonintegrable. To show this we use an extension of Ziglin theory made by Morales-Ruiz and Ramis. © 2001 American Institute of Physics.
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    Lie aspects of the dynamics of self-gravitating ellipsoids in n dimensions (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1761-1778 
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    Notes: In this paper we study the dynamics of self-gravitating ellipsoids in n dimensions, from the point of view of the Poisson structure of the dual of a suitable Lie algebra. When n=3 this was done by Rosenteel. In this setting we describe explicitly the ring of invariant functions. In the two-dimensional case we apply a technique due to Pedersen to find globally defined Darboux coordinates on the coadjoint orbits. Finally we derive a characterization of tensors coming from potentials, and use it to exhibit the dynamical equations of the ellipsoid in the Hamiltonian form. © 2001 American Institute of Physics.
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    Integration of a generalized Hénon–Heiles Hamiltonian (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1906-1915 
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    Notes: The generalized Hénon–Heiles Hamiltonian H=1/2(PX2+PY2+c1X2+c2Y2)+aXY2−bX3/3 with an additional nonpolynomial term μY−2 is known to be Liouville integrable for three sets of values of (b/a,c1,c2). It has been previously integrated by genus two theta functions only in one of these cases. Defining the separating variables of the Hamilton–Jacobi equations, we succeed here, in the two other cases, to integrate the equations of motion with hyperelliptic functions. © 2002 American Institute of Physics.
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    Generalized sine-Gordon/massive Thirring models and soliton/particle correspondences (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1916-1937 
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    Notes: We consider a real Lagrangian off-critical submodel describing the soliton sector of the so-called conformal affine sl(3)(1) Toda model coupled to matter fields. The theory is treated as a constrained system in the context of Faddeev–Jackiw and the symplectic schemes. We exhibit the parent Lagrangian nature of the model from which generalizations of the sine-Gordon (GSG) or the massive Thirring (GMT) models are derivable. The dual description of the model is further emphasized by providing the relationships between bilinears of GMT spinors and relevant expressions of the GSG fields. In this way we exhibit the strong/weak coupling phases and the (generalized) soliton/particle correspondences of the model. The sl(n)(1) case is also outlined. © 2002 American Institute of Physics.
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    A parabolic approximation method with application to global wave propagation (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1875-1905 
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    Notes: Motivated by the difficulty in using the splitting matrix method to obtain parabolic approximations to complicated wave equations, we have developed an alternative method. It is three dimensional, does not a priori assume a preferred direction or path of propagation in the horizontal, determines spreading factors, and results in equations that are energy conserving. It is an extension of previous work by several authors relating parabolic equations to the horizontal ray acoustics approximation. Unlike previous work it applies the horizontal ray acoustics approximation to the propagator rather than to the Green's function or the homogenous field. The propagator is related to the Green's function by an integral over the famous "fifth parameter" of Fock and Feynman. Methods for evaluating this integral are equivalent to narrow-angle approximations and their wide-angle improvements. When this new method is applied to simple problems it gives the standard results. In this paper it is described by applying it to a problem of current interest—the development of a parabolic approximation for modeling global underwater and atmospheric acoustic propagation. The oceanic or atmospheric waveguide is on an Earth that is modeled as an arbitrary convex solid of revolution. The method results in a parabolic equation that is energy conserving and has a spreading factor that describes field intensification for antipodal propagation. Significantly, it does not have the singularities in its range-sliced version possessed by many parabolic equations developed for global propagation. We then discuss two extensions of the method; first to propagation along refracted geodesics and second to a description involving discrete, local, normal modes.
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    The Lund–Regge surface and its motion's evolution equation (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1938-1955 
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    Notes: The system of evolution equations for general motion of surfaces in orthogonal coordinates is analyzed to reduce the number of variables as well as equations. The explicit expression of the Lund–Regge surface is obtained. When the surface corresponds to the Lund–Regge equation, we prove that some components of velocity satisfy the linearizations of the Lund–Regge equation. The soliton solution is derived and one special case of the Lund–Regge surface is studied. © 2002 American Institute of Physics.
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    Path integral for relativistic Aharonov–Bohm–Coulomb system on the pseudo-sphere (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1053-1065 
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    Notes: The Green's function for relativistic spinless Aharonov–Bohm–Coulomb (ABC) system on the pseudo-sphere Λ(2) is calculated using Kleinert's path integral representation for relativistic spinless particles. The energy spectrum and the corresponding wave functions are extracted for bound and scattering states. The results in the nonrelativistic and flat space limits are considered. © 2001 American Institute of Physics.
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    Nöther charges, Brown–York quasilocal energy, and related topics (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1173-1195 
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    Notes: The Lagrangian proposed by York et al. and the covariant first-order Lagrangian for general relativity are reviewed. They both deal with the (vacuum) gravitational field on a reference background and were conjectured to be equivalent. The two corresponding actions are compared and we show that the first one can in fact be obtained from the latter under suitable hypotheses. A conditioned correspondence among Nöther conserved quantities of covariant first-order Lagrangian, Brown–York quasilocal energy and the standard ADM Hamiltonian is also established. © 2001 American Institute of Physics.
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    On combined standard–nonstandard or hybrid (q,h)-deformations (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1236-1249 
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    Notes: Combined (q,h)-deformations proposed by Kupershmidt and Ballesteros–Herranz–Parashar are studied. In each case a transformation is shown to lead to an equivalent, standard q-deformation. We briefly indicate that appropriate singular limits of the same type of transformations can however lead from standard biparametric (p,q)-deformations to nonhybrid but biparametric nonstandard (g,h) ones. Finally a case of hybrid (q,h)-deformation is recalled, related to the superalgebra GL(1|1). © 2001 American Institute of Physics.
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    Differential geometry of GLh(1|1) (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1283-1295 
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    Notes: We construct a differential calculus on the quantum supergroup GLh(1|1) and obtain the h-deformed superalgebra of GLh(1|1). © 2001 American Institute of Physics.
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    Recursion operators of some equations of hydrodynamic type (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1309-1325 
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    Notes: We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N=2 and N=3 containing the equations of shallow water waves and its generalizations with their first two general symmetries and their recursion operators. We also discuss a reduction of N+1 systems to N systems of some new equations of hydrodynamic type. © 2001 American Institute of Physics.
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    Quotient of a loop group and Witten genus (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1364-1383 
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    Notes: We define a Dirac–Ramond operator over the quotient (LG)/H of a loop group by a subgroup H of the compact Lie group G. We state the conjecture that its equivariant Index with respect of the natural circle action over the quotient of the loop group is equal to the Witten genus of the homogeneous manifold G/H. We motivate the conjecture by a short time argument which allows to come back to a Dirac–Ramond operator at the manner of Taubes on a limit model where all the computations can be done by hand. © 2001 American Institute of Physics.
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    To the Gel'fand–Tsetlin realization of irreducible representations of classical semisimple algebras (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1384-1396 
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    Notes: It is shown that the Gel'fand–Tsetlin realization of irreducible representations of the An algebra is directly connected with a linear exactly integrable system in the n-dimensional space. General solutions for this system is explicitly given. © 2001 American Institute of Physics.
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    Stability of nonconservative hyperbolic systems and relativistic dissipative fluids (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1426-1442 
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    Notes: A stability theorem for general quasi-linear symmetric hyperbolic systems (not necessarily conservation laws) is proved in this work. The key assumption is the "stability eigenvalue condition," which requires all the eigenvalues of the constant coefficient system symbol to have negative real part for nonzero Fourier frequency, decaying no faster than |ω|2 when |ω|→0. The decay of the solution to zero, as time grows to infinity, is proved when the space dimension is bigger than or equal to 3. As an application of the general theorem, stability is proved for the equations describing relativistic dissipative fluids. © 2001 American Institute of Physics.
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    Deformation of surfaces, integrable systems, and Chern–Simons theory (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1397-1417 
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    Notes: A few years ago, some of us devised a method to obtain integrable systems in (2+1)-dimensions from the classical non-Abelian pure Chern–Simons action via the reduction of the gauge connection in Hermitian symmetric spaces. In this article we show that the methods developed in studying classical non-Abelian pure Chern–Simons actions can be naturally implemented by means of a geometrical interpretation of such systems. The Chern–Simons equation of motion turns out to be related to time evolving two-dimensional surfaces in such a way that these deformations are both locally compatible with the Gauss–Mainardi–Codazzi equations and completely integrable. The properties of these relationships are investigated together with the most relevant consequences. Explicit examples of integrable surface deformations are displayed and discussed. © 2001 American Institute of Physics.
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    On the problem of algebraic completeness for the invariants of the Riemann tensor: I (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1474-1485 
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    Notes: We present a new determining set, CZ, of Riemann invariants which possesses the minimum degree property. From an analysis on the possible independence of CZ, we are led to the division of all space–times into two distinct, invariantly characterized, classes: a general class MG+, and a special, singular class MS. For each class, we provide an independent set of invariants (IG+⊂CZ and IS⊂CZ, respectively) which, with the results of a sequel paper, will be shown to be algebraically complete. © 2001 American Institute of Physics.
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    Ground state energy of massive scalar field inside a spherical region in the global monopole background (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 562-581 
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    Notes: Using the zeta function regularization method we calculate the ground state energy of scalar massive field inside a spherical region in the space–time of a pointlike global monopole. Two cases are investigated: (i) First, we calculate the Casimir energy inside a sphere of radius R and analyze the obtained result. We observe that this energy may be positive or negative depending on metric coefficient α and nonconformal coupling ξ. In the limit R→∞, this energy vanishes: (ii) In the second model, we surround the monopole by an additional sphere of radius r0〈R and consider the scalar field confined in the region between these two spheres. In this case, the ground state energy presents an additional contribution due to boundary at r0 which is divergent for small radius. Additional comments about renormalization are considered. © 2001 American Institute of Physics.
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    Relativistic N-boson systems bound by oscillator pair potentials (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1237-1246 
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    Notes: We study the lowest energy E of a relativistic system of N identical bosons bound by harmonic-oscillator pair potentials in three spatial dimensions. In natural units (h-dash-bar)=c=1 the system has the semirelativistic (or "spinless-Salpeter") Hamiltonian, H=∑i=1Nm2+pi2+∑j〉i=1Nγ|ri−rj|2, γ〉0. We derive the following energy bounds: E(N)=minr〉0[N(m2+2(N−1)P2/(Nr2))1/2+(N/2)(N−1)γr2], N≥2, where P=1.376 yields a lower bound and P=〈fraction SHAPE="CASE"〉32 yields an upper bound for all N≥2. A sharper lower bound is given by the function P=P(m) which makes the formula for E(2) exact: with this choice of P, the bounds coincide for all N≥2 in the Schrödinger limit defined by m→∞. © 2002 American Institute of Physics.
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    Symmetry properties and explicit solutions of the generalized Weierstrass system (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1250-1282 
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    Notes: The method of symmetry reduction is systematically applied to derive several classes of invariant solutions for the generalized Weierstrass system inducing constant mean curvature surfaces and to the associated two-dimensional nonlinear sigma model. A classification of subgroups with generic orbits of codimension one of the Lie point symmetry group for these systems provides a tool for introducing symmetry variables and reduces the initial systems to different nonequivalent systems of ordinary differential equations. We perform a singularity analysis for them in order to establish whether these ordinary differential equations have the Painlevé property. These ordinary differential equations can then be transformed to standard forms and next solved in terms of elementary and Jacobi elliptic functions. This results in a large number of new solutions and in some cases new interesting constant mean curvature surfaces are found. Furthermore, this symmetry analysis is extended to include conditional symmetries by subjecting the original system to certain differential constraints. In this case, several new types of nonsplitting algebraic, trigonometric, and hyperbolic multisoliton solutions have been obtained in explicit form. Some physical interpretation of these results in the areas of fluid membranes, string theory, two-dimensionl gravity, and cosmology are given. © 2001 American Institute of Physics.
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    Diagram projection rules for recoupling diagrams in the Racah–Wigner category (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1346-1363 
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    Notes: This paper gives three important techniques for recoupling coefficients of an arbitrary number or irreducible representations: factorization as a product of smaller degree recoupling coefficients, diagram projection projecting a recoupling diagram to obtain constraints on recoupling coefficients, and primitive expansion expressing a recoupling coefficient in terms of primitive recoupling coefficients. The first technique reduces a recoupling coefficient to its essential and simplest form. The second is many faceted allowing one to work at the recoupling level. Importantly, recoupling diagrams can be used to construct a complete set of constraints on the recoupling coefficients. The third allows large degree recoupling coefficients to be expressed in terms of primitive recoupling coefficients. An example of this is the fact that the 9j symbol is defined by the 3j and 6j symbols. © 2001 American Institute of Physics.
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    Harmonic functions and angular momentum for anyon systems (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1418-1425 
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    Notes: A method of construction of harmonic functions for the system of anyons on a plane is given. Spectra of angular momentum are derived. Anyonic statistics implies a restriction of the range of angular momentum which is stronger in comparison to the bosonic and fermion case. © 2001 American Institute of Physics.
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    Painlevé–Calogero correspondence revisited (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1443-1473 
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    Notes: We extend the work of Fuchs, Painlevé and Manin on a Calogero-like expression of the sixth Painlevé equation (the "Painlevé–Calogero correspondence") to the other five Painlevé equations. The Calogero side of the sixth Painlevé equation is known to be a nonautonomous version of the (rank one) elliptic model of Inozemtsev's extended Calogero systems. The fifth and fourth Painlevé equations correspond to the hyperbolic and rational models in Inozemtsev's classification. Those corresponding to the third, second and first are not included therein. We further extend the correspondence to the higher rank models, and obtain a "multi-component" version of the Painlevé equations. © 2001 American Institute of Physics.
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    Spherically symmetric solutions of the sixth order SU(N) Skyrme models (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5580-5595 
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    Notes: Following the construction described by Ioannidou et al. [J. Math. Phys. 40, 6353 (1999)], we use the rational map ansatz to construct analytically some topologically nontrivial solutions of the generalized SU(3) Skyrme model defined by adding a sixth order term to the usual Lagrangian. These solutions are radially symmetric and some of them can be interpreted as bound states of Skyrmions. The same ansatz is used to construct low-energy configuration of the SU(N) Skyrme model. © 2001 American Institute of Physics.
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    Investigation of the relativistic equivalent Hamiltonian in the LS coupling scheme (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5642-5651 
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    Notes: Armstrong's method of relativistic description of atoms in LS coupling using the equivalent operator is developed. Its form in terms of standard unit operators acting within a space of one shell is obtained. The interpretation of separate terms of equivalent Breit operator is investigated in a general case of nonequivalent electrons. The relativistic Dirac–Fock equations for the level and term in LS coupling are derived. The equivalent operator is applied to obtain the averages of relativistic operators too. © 2001 American Institute of Physics.
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    Asymptotics for the condensate multivortex solutions in the self-dual Chern–Simons CP(1) model (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5698-5712 
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    Notes: In this paper we study the asymptotics for the condensate multivortex solutions in the self-dual Chern–Simons CP(1) model. When the breaking parameter s belongs to (−〈fraction SHAPE="CASE"〉12,〈fraction SHAPE="CASE"〉12), we show that for any sequence of multivortex solutions which lies between suitable super- and subsolutions with respect to the Chern–Simons coupling constant κ, we can find a subsequence which converges to a constant depending only on s as κ goes to zero. Also we investigate the locally uniform convergence speed. © 2001 American Institute of Physics.
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    Three formulas for the off-diagonal density matrix of a dirac spinor, with an application (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 674-685 
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    Notes: Expressions for the off-diagonal density matrix of a Dirac spinor in space–time dimensions 2, 3, and 4 are derived. They are used to obtain formulas for the dual potential of a free Dirac current in two, three, and four dimensions of space–time. © 2001 American Institute of Physics.
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    Thermodynamics of trapped interacting bosons in one dimension (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 765-772 
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    Notes: On the basis of Bethe ansatz solution of bosons with δ-function interaction in a one-dimensional potential well, the thermodynamics equilibrium of the system in finite temperature is studied by using the strategy of Yang and Yang. The thermodynamics quantities, such as specific heat, etc., are obtained for the cases of the strong coupling and weak coupling limits respectively. © 2001 American Institute of Physics.
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    Large N limit of SO(N) scalar gauge theory (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1340-1352 
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    Notes: In this paper we study the large Nc limit of SO(Nc) gauge theory coupled to a real scalar field following ideas of Rajeev [Int. J. Mod. Phys. A 9, 5583 (1994)]. We will see that the phase space of this resulting classical theory is Sp1(H)/U(H+) which is the analog of the Siegel disk in infinite dimensions. The linearized equations of motion give us a version of the well-known 't Hooft equation of two dimensional quantum chromodynamics. © 2002 American Institute of Physics.
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    High order relativistic corrections to Keplerian motion (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 839-855 
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    Notes: The first terms of the general solution for an asymptotically flat stationary axisymmetric vacuum spacetime endowed with an equatorial symmetry plane are calculated from the corresponding Ernst potential up to seventh order in the radial pseudospherical coordinate. The metric is used to determine the influence of high order multipoles in the perihelion precession of an equatorial orbit and in the node line precession of a nonequatorial orbit with respect to a geodesic circle. Both results are written in terms of invariant quantities such as the Geroch–Hansen multipoles and the energy and angular momentum of the orbit. © 2001 American Institute of Physics.
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    Petrov type D Einstein space–times of embedding class two (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 863-875 
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    Notes: A space–time is of embedding class 2 if its curvature tensor can be written in terms of two symmetric tensors aαβ and bαβ which satisfy the Gauss, Codazzi, and Ricci equations. For an Einstein space–time the Ricci tensor is proportional to the metric tensor. Using the Petrov classification of the curvature tensor and canonical forms of aαβ and bαβ, this paper produces a list of the embedding class 2 Petrov type D Einstein space–times. After a summary of the basic equations and the previous work on embedding class 2 space–times, the field equations for Einstein space–times are expressed in a canonical form and the type D Petrov conditions applied. The resulting equations are solved and give two sets of metrics. The first are known metrics which are products of two 2-spaces of constant curvature and the second set is a generalization of the Kottler solution. The form of the second set of solutions depends upon whether the metric depends upon one or two of the four coordinates. © 2001 American Institute of Physics.
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    Batalin–Tyutin quantization of the spinning particle model (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5202-5211 
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    Notes: The spinning particle model for anyon is analyzed in the Batalin–Tyutin scheme of quantization in extended phase space. Here additional degrees of freedom are introduced in the phase space such that all the constraints in the theory are rendered first class, that is, commuting in the sense of Poisson brackets. Thus the theory can be studied without introducing the Dirac brackets which appear in the presence of noncommuting or second class constraints. In the present case the Dirac brackets make the configuration space of the anyon noncanonical and also, being dynamical variable dependent, poses problems for the quantization program. We show that previously obtained results (e.g., gyromagnetic ratio of anyon being 2) are recovered in the Batalin–Tyutin variable independent sector in the extended space. The Batalin–Tyutin variable contributions are significant and are computable in a straightforward manner. The latter can be understood as manifestations of the noncommutative space–time in the enlarged phase space. © 2001 American Institute of Physics.
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    Representations of the q-deformed algebra Uq′(so4) (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5389-5416 
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    Notes: We study the nonstandard q-deformation Uq′(so4) of the universal enveloping algebra U(so4) obtained by deforming the defining relations for skew-symmetric generators of U(so4). This algebra is used in quantum gravity and algebraic topology. We construct a homomorphism φ of Uq′(so4) to the certain nontrivial extension of the Drinfeld–Jimbo quantum algebra Uq(sl2)⊗2 and show that this homomorphism is an isomorphism. By using this homomorphism we construct irreducible finite-dimensional representations of the classical type and of the nonclassical type for the algebra Uq′(so4). It is proved that for q not a root of unity each irreducible finite-dimensional representation of Uq′(so4) is equivalent to one of these representations. We prove that every finite-dimensional representation of Uq′(so4) for q not a root of unity is completely reducible. It is shown how to construct (by using the homomorphism φ) tensor products of irreducible representations of Uq′(so4). [Note that no Hopf algebra structure is known for Uq′(so4).] These tensor products are decomposed into irreducible constituents. © 2001 American Institute of Physics.
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    Soliton solutions of XXZ lattice Landau–Lifshitz equation (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5457-5471 
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    Notes: Multisoliton solutions of the partially isotropic (classical) lattice Landau–Lifshitz equation are constructed. A trigonometric version of the dressing method is proposed to this aim. The dressing matrix is a matrix valued periodic function of the spectral parameter, and takes almost the same form as the L-matrix except for the number of poles. Both the easy-axis (J1=J2〈J3) and easy-plane (J1〈J2=J3) cases can be treated in a parallel way. © 2001 American Institute of Physics.
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    Erratum: "Hyperbolic Kac–Moody algebra from intersecting p-branes" [J. Math. Phys. 40, 4072 (1999)] (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5493-5493 
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    Notes: © 2001 American Institute of Physics.
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    Instantons in four-dimensional gauged O(5) Skyrme models (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4669-4683 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider a family of four-dimensional nonlinear sigma models based on an O(5) symmetric group, whose fields take their values on the 4-sphere S4. An SO(4)-subgroup of the model is gauged. The solutions of the model are characterized by two distinct topological charges, the Chern–Pontryagin charge of the gauge field and the degree of the map, i.e., the winding number, of the S4 field. The one-dimensional equations arising from the variation of the action density subjected to spherical symmetry are integrated numerically. Several properties of the solutions thus constructed are pointed out. The only solution with unit Chern–Pontryagin charge are the usual BPST instantons with zero S4 winding number, while solutions with unit S4 winding number have zero Chern–Pontryagin charge. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1396636
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    The disorder deviation in the deconfined phase (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4749-4756 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A systematic study of the strongly interacting matter under extreme conditions via the form of the thermal ratio of the disorder deviation is presented. The evolution of Fermi and Bose particles (quarks and gluons) is studied in the framework of multi-particle correlation and distribution functions to predict the size of the finite-temperature deconfined phase. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1387467
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    Symmetries in the Hubbard model with n-fold orbital degeneracy (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4865-4872 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The present paper studies the symmetries of the Hubbard model of electrons with generally n-fold orbital degeneracy. It is shown that SUd(2n) and SUc(2n) symmetries hold, respectively, for the model with completely repulsive or attractive on-site interaction and that with partly attractive interactions. An extended Lieb–Mattis transformation is given to map these two symmetries into each other. The subsymmetry SUd(e)(n)⊗SUd(o)(n) is found to be shared by the two models with arbitrary chemical potential μ. By assuming at most two electrons on each site it is found that SUd(2n)P and SUc(2n)P both exist in each kind of the two models and consequently lead to a larger symmetry SUd(2n)P×SUc(2n)P. Another underlying symmetry (SUc(e)(2)P×(centered ellipsis)×SUc(e)(2)P)⊗(SUc(o)(2)P×(centered ellipsis)×SUc(o)(2)P) is also revealed for the unified U model under the excluding. The symmetry is valid for the partially attractive model with chemical potential μ=−U. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1402956
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    Graphical representation of the partition function of a one-dimensional δ-function Bose gas (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4883-4893 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The one-dimensional repulsive δ-function bose system is studied. By only using the Bethe ansatz equation, n-particle partition functions are exactly calculated. From this expression for the n-particle partition function, the n-particle cluster integral is derived. The results completely agree with those of the thermal Bethe ansatz (TBA). This directly proves the validity of the TBA. The theory of partitions and graphs is used to simplify the discussion. © 2001 American Institute of Physics.
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    The methods of gluing manifolds in general relativity (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1519-1535 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Some areas of modern theoretical physics such as modern cosmology contain different manifolds which must be glued together along a common boundary. These boundaries can be spacelike, timelike, or lightlike hypersurfaces. This paper shows how this gluing for different hypersurfaces is possible. Two different approaches are considered and the extent to which these approaches are equivalent are discussed. In particular, we will construct a distributional approach for dynamics of lightlike hypersurfaces in general relativity. Since Einstein's equations are nonlinear PDEs, for discontinuous metrics such as signature changing metrics, product of distributions are unavoidable. To glue two different manifolds which admit signature change, we consider this problem in the context of Colombeau's new theory of generalized functions. Some examples are given for clarification. © 2002 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1452758
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    The multiple sum formulas for 12j coefficients of SU(2) and uq(2) (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1547-1568 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The expressions for 12j coefficients of the both kinds (without and with braiding) of the SU(2) group and the quantum algebra uq(2) are considered. Using Dougall's summation formula of the very well-poised hypergeometric 5F4(1) series and its q-generalization, several fourfold sum formulas [with each sum related to the balanced 5F4(1) or 5φ4 series] for the q-12j coefficients of the second kind (without braiding) are derived. Applying q-generalizations of rearrangement formulas of the very well-poised hypergeometric 6F5(−1) series [which correspond to a new expression for the Clebsch–Gordan coefficients of SU(2) and uq(2)], the new expressions with five sums [of the 4F3(1) and 3F2(1) or 4φ3 and 3φ2 type] are derived for the q-12j coefficients of the first kind (with braiding) instead of the usual expansions in terms of q-6j coefficients. Stretched and doubly stretched q-12j coefficients [as triple, double, or single sums, related to composed or separate hypergeometric 4F3(1) and 5F4(1) or 4φ3 and 5φ4 series and, particularly, to q-9j or q-6j coefficients] are considered.© 2002 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1436305
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    Understanding singularities in Cartan's and null surface formulation geometric structures (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1584-1597 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this work we establish a relationship between Cartan's geometric approach to third-order ordinary differential equations and the three-dimensional null surface formulation. We then generalize both constructions to allow for caustics and singularities that necessarily arise in these formalisms. © 2002 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1408282
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    Modified braid equations for SOq(3) and noncommutative spaces (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1569-1583 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: General solutions of the R(circumflex)TT equation with a maximal number of free parameters in the specrtal decomposition of vector SOq(3) R(circumflex) matrices are implemented to construct modified braid equations (MBE). These matrices conserve the given, standard, group relations of the nine elements of T, but are not constrained to satisfy the standard braid equation (BE). Apart from q and a normalization factor our R(circumflex) contains two free parameters, instead of only one such parameter for deformed unitary algebras studied in a previous paper [Math. QA/0009178] where the nonzero right hand side of the MBE had a linear term proportional to (R(circumflex)(12)−R(circumflex)(23)). In the present case the rhs is, in general, nonlinear. Several particular solutions are given (Sec. II) and the general structure is analyzed (Appendix A). Our formulation of the problem in terms of projectors yields also two new solutions of standard (nonmodified) braid equation (Sec. II) which are further discussed (Appendix B). The noncommutative three-spaces obtained by implementing such generalized R(circumflex) matrices are studied (Sec. III). The role of coboundary R(circumflex) matrices (not satisfying the standard BE) is explored. The MBE and Baxterization are presented as complementary facets of the same basic construction, namely, the general solution of R(circumflex)TT equation (Sec. IV). A new solution is presented in this context. As a simple but remarkable particular case a nontrivial solution of BE is obtained (Appendix B) for q=1. This solution has no free parameter and is not obtainable by twisting the identity matrix. In the concluding remarks (Sec. V), among other points, generalization of our results to SOq(N) is discussed. © 2002 American Institute of Physics.
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    Solution of a second order difference equation using the bilinear relations of Riemann (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1598-1621 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A recently proposed technique to solve a class of second order functional difference equations arising in electromagnetic diffraction theory is further investigated by applying it to a case of intermediate complexity. The proposed approach is conceptually simple and relies on first obtaining well-defined branched solutions to a pair of associated first order difference equations. The construction of these branched expressions leads to an equation system whose solution requires relationships akin to Riemann's bilinear relations for differentials of the first and third kinds; their derivation necessitates the application of Cauchy's theorem on Riemann surfaces of, in this particular instance, genera one and three. Branch-free solutions of the second order difference equation are then obtained by taking appropriate linear combinations of the branched solutions of the first order equations. Analysis and computation demonstrate that the resulting expressions have the desired analytical properties and recover known solutions in the appropriate limit. © 2002 American Institute of Physics.
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    Transformation formulas for double hypergeometric series related to 9-j coefficients and their basic analogs (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5417-5430 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In a recent paper, Ališauskas deduced different triple sum expressions for the 9-j coefficient of su(2) and suq(2). For a singly stretched 9-j coefficient, these reduce to different double sum series. Using these distinct series, we deduce a set of new transformation formulas for double hypergeometric series of Kampé de Fériet type and their basic analogs. These transformation formulas are valid for rather general parameters of the series, although a common feature is that all the series appearing here are terminating. It is also shown that the transformation formulas deduced here generate a group of transformation formulas, thus yielding an invariance group or symmetry group of particular double series. © 2001 American Institute of Physics.
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    Families of particular solutions to multidimensional partial differential equations (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5472-5492 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Dressing methods are known as productive tools for construction of the particular solutions to the big class of nonlinear partial differential equations (PDEs) which are integrable by the inverse scattering technique. Recently the modification of the dressing method based on the system of algebraic equations has been suggested which allows us to find the families of particular solutions to certain types of nonintegrable (in classical sense) nonlinear PDEs. This modification represents PDEs as closure reductions of an appropriate differential-difference system. In this article we study the dressing procedure in more detail. Particularly, we consider different families of particular solutions available through the dressing method based on the algebraic system. We give two examples of the differential-difference systems and related PDEs and point to other possible generalizations of the dressing method. © 2001 American Institute of Physics.
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    Algebraic treatment of super-integrable potentials (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4684-4706 
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    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The so(2,1) Lie algebra is applied to three classes of two- and three-dimensional Smorodinsky–Winternitz super-integrable potentials for which the path integral discussion has been recently presented in the literature. We have constructed the Green's functions for two important super-integrable potentials in R2. Among the super-integrable potentials in R3, we have considered two examples, one is maximally super-integrable and another one minimally super-integrable. The discussion is made in various coordinate systems. The energy spectrum and the suitably normalized wave functions of bound and continuous states are then deduced. © 2001 American Institute of Physics.
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    Creation operators and Bethe vectors of the osp(1|2) Gaudin model (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4757-4778 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A Gaudin model based on the orthosymplectic Lie superalgebra osp(1|2) is studied. The eigenvectors of the osp(1|2) invariant Gaudin Hamiltonians are constructed by algebraic Bethe ansatz. Corresponding creation operators are defined by a recurrence relation. Furthermore, explicit solution to this recurrence relation is found. The action of the creation operators on the lowest spin vector yields Bethe vectors of the model. The relation between the Bethe vectors and solutions to the Knizhnik–Zamolodchikov equation of the corresponding super-conformal field theory is established. © 2001 American Institute of Physics.
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    n-symplectic algebra of observables in covariant Lagrangian field theory (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4827-4845 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: n-symplectic geometry on the adapted frame bundle λ:LπE→E of an n=(m+k)-dimensional fiber bundle π:E→M is used to set up an algebra of observables for covariant Lagrangian field theories. Using the principle bundle ρ:LπE→J1π we lift a Lagrangian L:J1π→R to a Lagrangian L:=ρ*(L):LπE→R, and then use L to define a "modified n-symplectic potential" θ(circumflex)L on LπE, the Cartan–Hamilton–Poincaré (CHP) Rn-valued 1-form. If the lifted Lagrangian is nonzero, then (LπE,dθ(circumflex)L) is an n-symplectic manifold. To characterize the observables we define a lifted Legendre transformation φL from LπE into LE. The image QL:=φL(LπE) is a submanifold of LE, and (QL,d(θ(circumflex)|QL)) is shown to be an n-symplectic manifold. We prove the theorem that θ(circumflex)L=φL*(θ|QL), and pull back the reduced canonical n-symplectic geometry on QL to LπE to define the algebras of observables on the n-symplectic manifold (LπE,dθ(circumflex)L). To find the reduced n-symplectic algebra on QL we set up the equations of n-symplectic reduction, and apply the general theory to the model of a k-tuple of massless scalar fields on Minkowski space–time. The formalism set forth in this paper lays the ground work for a geometric quantization theory of fields. © 2001 American Institute of Physics.
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    Proof of a conjecture on the conductivity of checkerboards (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4873-4882 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In 1985 Mortola and Steffé conjectured a formula for the effective conductivity tensor of a checkerboard structure where the unit cell of periodicity is square and subdivided into four equal squares each having a different conductivity. In this article their conjecture is proven. The key idea is to superimpose suitably reflected potentials to obtain the solution to the dual problem. This is then related back to the original problem using a well known theorem of Keller, thereby proving the conjecture. The analysis also yields formulas relating the potentials in the four squares. Independently, Craster and Obnosov have obtained a completely different proof of the conjecture. © 2001 American Institute of Physics.
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    Calogero–Moser systems with periodic and doubly periodic interaction potentials and loop algebras (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4927-4937 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For a finite number of particles on the line pairwise interacting with 1/r2 potential, the positions are given by the eigenvalues of some time-dependent matrix. Infinite periodic or doubly periodic replication of the particles yields Calogero–Moser systems with periodic or doubly periodic interaction potential. We are thus led to consider matrices of infinite order, which are identified with Fourier series with matrix coefficients, depending on an additional parameter. These distributional loops of matrices (tori of matrices in the doubly periodic case) are shown to obey simple (partial) differential equations, which allow us to determine them explicitly. Thus we obtain the already known solution of the Calogero–Moser system on the circle, and provide a new insight for the system on the torus. © 2001 American Institute of Physics.
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    Effect of couplings weakening and reversing in ferromagnetic Ising systems— Rigorous inequalities (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 6090-6092 
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    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider Ising systems where all the many-spin couplings JA are positive. We show that the absolute value of all the many-spin correlations does not increase when the value of any of the couplings is reduced, taking any value in the interval [−JA,JA]. Results of this type are motivated by work in systems such as random field Ising models. © 2000 American Institute of Physics.
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    Invariant subspaces of the periodic Navier–Stokes and magnetohydrodynamics equations: Symmetries and inverse cascades (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 6193-6197 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that when the initial condition and the forcing term of the periodic Navier–Stokes or magnetohydrodynamics equations have Fourier coefficients which vanish outside a certain semigroup of frequencies, the same happens to the solutions for all time. Subgroups of frequencies correspond to solutions possessing certain symmetries. By taking as a semigroup the frequencies whose Fourier components are non-negative integers, we get a class of solutions for which the higher modes do not influence the evolution of the lower ones; therefore, the phenomenon of inverse cascading cannot occur for them. © 2000 American Institute of Physics.
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    Expansion in the distance parameter for two vortices close together (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 182-191 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Static vortices close together are studied for two different models in two-dimensional Euclidean space. In a simple model for one complex field, an expansion in the parameters describing the relative position of two vortices can be given in terms of trigonometric and exponential functions. The results are then compared to those of the Ginzburg–Landau theory of a superconductor in a magnetic field at the point between type-I and type-II superconductivity. For the angular dependence a similar pattern emerges in both models. The differences for the radial functions are studied up to third order. © 2001 American Institute of Physics.
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    Nonlinear Schrödinger-type equations from multiscale reduction of PDEs. I. Systematic derivation (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 6399-6443 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this article we begin a systematic investigation via multiscale expansions of nonlinear evolution PDEs (partial differential equations). In this first article we restrict consideration to a single, autonomous, but otherwise generic, PDE in 1+1 variables (space+time), of first order in time, whose linear part is dispersive, and to solutions dominated by a single plane wave satisfying the linear part of the PDE. The expansion parameter is an, assumedly small, coefficient multiplying this plane wave. The main (indeed, asymptotically exact) effect of the (weak) nonlinearity is then to cause a modulation of the amplitude of the plane wave and of its harmonics, which is generally described, in (appropriately defined) coarse-grained time and space variables, by evolution equations of nonlinear Schrödinger type. A systematic analysis of such equations is presented, corresponding to various assumptions on the "resonances" occurring for the first few harmonics. © 2000 American Institute of Physics.
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    On a class of invariant coframe operators with application to gravity (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 6318-6340 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Let a differential 4D-manifold with a smooth coframe field be given. Consider the operators on it that are linear in the second order derivatives and quadratic in the first order derivatives of the coframe, both with coefficients that depend on the coframe variables. The article exhibits the class of operators that are invariant under a general change of coordinates, and, also, invariant under the global SO(1,3)-transformation of the coframe. A general class of field equations is constructed. We display two subclasses in it. The subclass of field equations that are derivable from action principles by free variations and the subclass of field equations for which spherical-symmetric solutions, Minkowskian at infinity, exist. Then, for the spherical-symmetric solutions, the resulting metric is computed. Invoking the geodesic postulate, we find all the equations that are experimentally (by the three classical tests) indistinguishable from Einstein field equations. This family also includes, of course, Einstein equations. Moreover, it is shown, explicitly, how to exhibit it. The basic tool employed in the article is an invariant formulation reminiscent of Cartan's structural equations. The article sheds light on the possibilities and limitations of the coframe gravity. It may also serve as a general procedure to derive covariant field equations. © 2000 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1287434
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