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  • Articles  (474)
  • American Institute of Physics (AIP)  (474)
  • Periodicals Archive Online (PAO)
  • 1995-1999
  • 1985-1989  (474)
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  • 1985  (474)
  • 1954
  • Mathematics  (474)
  • 1
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    Static relativistic perfect fluids with spherical, plane, or hyperbolic symmetry (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2268-2274 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This article examines the Einstein field of equations of general relativity, when the source of the gravitational field is a perfect fluid, and the geometry is static and possesses spherical, plane, or hyperbolic symmetry. This examination unifies, extends, and amends some earlier works. It is shown that a previous qualitative treatment of static spherically symmetric perfect fluids that obey a γ-law equation of state can be extended to include the cases of plane and hyperbolic symmetry. In the case of plane symmetry, the exact solution is provided for general values of γ. This indicates defects in an earlier prescription that was given for a general equation of state.
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    URL: http://dx.doi.org/10.1063/1.526807
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  • 2
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    Relativistic, stationary, axisymmetric perfect fluids. II. Solutions with vanishing magnetic Weyl tensor (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2279-2281 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The formalism of the previous article is used to obtain solutions of Einstein's field equations for the interior of a rigidly rotating perfect fluid, with zero magnetic Weyl tensor. It is found that these solutions cannot represent isolated rotating masses.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526809
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  • 3
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    On the asymptotics of distributions with support in cone (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2335-2341 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The asymptotic behaviors of tempered distributions with support in a convex, closed cone are classified by means of group theory. The notion of regularly varying distribution is introduced. An Abelian–Tauberian theorem for regularly varying tempered distributions, which generalizes the one-dimensional Abelian–Tauberian theorem of Hardy–Littlewood–Karamata and the many-dimensional extension due to Vladimirov, is proved. Applications to n-point functions are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526817
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  • 4
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    The vector form of the neutrino equation and the photon neutrino duality (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2346-2349 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new form of the vector wave equation for a neutrino is derived that makes the relation to the massive case more transparent than that given by Reifler. Some new aspects of the photon neutrino duality are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526819
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  • 5
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    Convergent expansions for excited glueball masses in 2+1 strongly coupled lattice gauge theories (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2342-2345 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is known that the mass spectrum of a strongly coupled (β=2/g2 small) 2+1 Wilson action lattice gauge theory contains a mass m0∼−4 ln β and two excited masses m1, m2∼−6 ln β and that m0+4 ln β has a convergent expansion in powers of β. We show that m1, m2 admit convergent expansions of the form −6 ln β+r(β), where r(β) is analytic at β=0. Furthermore, a finite lattice algorithm is given for determining cn, the nth β=0 Taylor coefficient of r(β). Here, cn only depends on a finite number of β=0 Taylor series coefficients of the plaquette–plaquette, plaquette–double plaquette, and double plaquette–double plaquette truncated correlation functions at a finite number of points. For the gauge group Z2, by duality, m1, m2 map to bound states of the low-temperature Ising model; a possible relation between an increasing number of bound states and roughening is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526818
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  • 6
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    Statistical theory of scattering and propagation through a rough boundary–The Bethe–Salpeter equation and applications (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2352-2369 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A systematic theory is given for a general class of scalar waves by introducing a surface Green's function, which is a 2×2 matrix function governed by boundary equations, transferred onto two reference boundary planes enclosing the real boundary inside. It is subjected to several symmetries, including a relation eventually leading to optical relations. Governing equations of statistical surface Green's functions of first and second orders are obtained unperturbatively in exactly the same way as for a random medium, on replacing the medium to a surface impedance. Two operator methods are introduced to obtain the surface impedance and integral equations of reflection–transmission coefficients exactly for a given boundary change. The space Green's functions outside the boundary are obtained by a simple continuation of the surface Green's functions, and scattering cross sections are obtained from their asymptotic expressions at large distances. Various quantities and equations associated with the incoherent waves are written exactly by the introduction of a scattering matrix, as contrasted with the conventional one for a coherent scatterer. A slightly rough boundary is investigated, with the cross sections for both reflected and transmitted waves, where obtained equations are significant also for higher-order effects, including multiple scattering. An application to boundary-value problems in layer transport is suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526821
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  • 7
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    Hamiltonian approach to the existence of magnetic surfaces (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2370-2380 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A method is devised to investigate the existence of magnetic surfaces and magnetohydrodynamic (MHD) plasma equilibria in 3-D toroidal geometry. The key feature of this method is the utilization of a Hamiltonian formulation of the lines of force. Expanding the contravariant components of the magnetic field and scalar pressure in distance ρ from the magnetic axis, the 1-D Hamiltonian for the lines of force is written out explicitly. The Hamiltonian is then transformed to action-angle variables. It is shown that the action J corresponds to pressure in the equilibrium problem. Specifically, it is shown that if J is an invariant, then constant pressure and hence magnetic surfaces exist. A procedure of repeated canonical transformations is formulated and carried out to displace the coordinate dependence in the Hamiltonian to successively higher order in the expansion parameter, and thus make J an increasingly better adiabatic invariant. Arising in each successive canonical transformation is a series of potentially resonant denominators, i.e., denominators that may vanish. These potential resonances are identified, their significance explicated, and methods of handling them suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526822
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  • 8
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    The continuity of dislocations (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2383-2385 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Dislocation continuity is derived from the Bilby–Kondo theory of dislocations using exterior calculus. Dislocation density is represented by the torsion vector-valued two-form. Burgers vectors are associated with the vector part of the torsion while dislocation lines are associated with the two-form part. The exterior derivative of the torsion is shown to vanish when the crystal curvature vanishes. This implies two simultaneous continuity conditions: Burgers vector conservation and continuity of dislocation lines. On the other hand, dislocation continuity is violated when the curvature does not vanish. Since this can occur on grain boundaries it is inferred that grain boundaries are regions where crystal curvature is concentrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526824
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  • 9
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    The adsorption of simple particles on a 2×N lattice space (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2392-2395 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Utilizing a 15-term recursion relation that describes exactly the composite nearest neighbor degeneracy for simple indistinguishable particles on a 2×N lattice, the adsorption isotherm is calculated and it is shown analytically that coverage as a function of the gas phase pressure exhibits no discontinuity, i.e., that no phase transition can occur.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526826
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  • 10
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    Canonical map approach to channeling stability in crystals (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1925-1935 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We state and prove rigorous mathematical results on the orbital stability of certain rectilinear trajectories of sufficiently energetic particles subjected to appropriate periodic potentials. This is done in the context of nontrivial classical Hamiltonian models, nonrelativistic and relativistic, in two space dimensions. The main steps involved in the proofs are the derivation of the asymptotic form of certain canonical maps in the plane in the limit of large particle energies and the application of a version of Moser's twist theorem. When suitably specialized, these results establish rigorously for the first time that the pertinent straight-line channeling trajectories of fast particles in two-dimensional rigid crystal lattices have this stability property under reasonable conditions on the crystal potential.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526859
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  • 11
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    On a particular solution of the equation of Ernst with n fields, parametrized by an arbitrary harmonic function (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1938-1941 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We determine a particular solution, dependent upon an arbitrary harmonic function in cylindrical coordinates, of the system of n partial differential equations, which characterizes both the axially symmetric field solution of the Einstein (n−1)–Maxwell equations and one class of axially symmetric static self-dual SU(n+1) Yang–Mills fields.
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    URL: http://dx.doi.org/10.1063/1.526975
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  • 12
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    Some remarks on torsion in Kaluza–Klein unification (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1942-1947 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The role of manifolds endowed with a parallelizing torsion in Kaluza–Klein theories is examined. In particular the spin connection on such manifolds is demonstrated to be a single pure gauge almost everywhere on the manifold. This follows from the Frobenius integration theorem. As a consequence of this result the computation of the representation of massless fermions follows immediately and trivially. The spectrum of massless fermions on manifolds with a parallelizing torsion is contrasted with the analogous spectrum on manifolds with nontrivial topological configurations. While the remarks are primarily of pedagogic value much of the relevant mathematics is made intuitive.
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    URL: http://dx.doi.org/10.1063/1.526861
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  • 13
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    On the one- and two-dimensional Toda lattices and the Painlevé property (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1956-1960 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Toda lattice and the two-dimensional Toda lattice (2-DTL) are shown to possess a type of "Painlevé property'' that is based on the use of separate "singular manifolds'' for each dependent variable. The isospectral problem for the 2-DTL found by both Mikhailov and by Fordy and Gibbons can be simply and logically derived from this analysis. Some remarks are made about the connection between our work and independent work of Kametaka and Airhault on the relationship between the Toda lattice and the second Painlevé transcendent.
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    URL: http://dx.doi.org/10.1063/1.526863
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  • 14
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    Concepts of conditional expectations in quantum theory (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1948-1955 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A concept of conditional expectations in quantum theory is established with interrelations to previously introduced concepts of the Cycon–Hellwig conditional expectations and a posteriori states, which are analogous to the existing interrelations in the classical probability theory among conditional expectations related to random variables, those related to σ subalgebras and conditional probability distributions. These three concepts are shown to have satisfactory statistical interpretation in the quantum measuring processes. For the above purpose, we introduce an integration with respect to functions with values in the states of operator algebras and positive operator valued measures such that the resulting indefinite integrals are completely positive map valued measures. Eventually, it is proved that in the von Neumann algebraic formulation, the Cycon–Hellwig conditional expectations always exist as completely positive map valued measures.
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    URL: http://dx.doi.org/10.1063/1.526862
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  • 15
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    Canonical transformations theory for presymplectic systems (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1961-1969 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We develop a theory of canonical transformations for presymplectic systems, reducing this concept to that of canonical transformations for regular coisotropic canonical systems. In this way we can also link these with the usual canonical transformations for the symplectic reduced phase space. Furthermore, the concept of a generating function arises in a natural way as well as that of gauge group.
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    URL: http://dx.doi.org/10.1063/1.526864
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  • 16
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    How to construct integrable Fokker–Planck and electromagnetic Hamiltonians from ordinary integrable Hamiltonians (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1970-1975 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Integrable Hamiltonians with velocity-dependent potentials, including those of Fokker–Planck-type H=1/2(p2x+p2y)+Kxpx+Kypy, are constructed from integrable Hamiltonians of type H=1/2(p2x+p2y)+V(x,y) using certain canonical and noncanonical transformations. Some of the Hamiltonians obtained this way are integrable only for zero energy. Candidates for the Φ potential, which is of interest for Fokker–Planck models, are constructed in several cases.
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    URL: http://dx.doi.org/10.1063/1.526865
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  • 17
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    Lax-pair operators for squared-sum and squared-difference eigenfunctions (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1976-1978 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An interrelationship between various representations of the inverse scattering transformation is established by examining eigenfunctions of Lax-pair operators of the sine–Gordon equation and the modified Korteweg–de Vries equation. In particular, it is shown explicitly that there exist Lax-pair operators for the squared-sum and squared-difference eigenfunctions of the Ablowitz–Kaup–Newell–Segur inverse scattering transformation.
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    URL: http://dx.doi.org/10.1063/1.526866
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  • 18
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    On the convergence of the Rytov approximation for the reduced wave equation (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1979-1985 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The reduced wave equation Δu+k2n2(x)u=0 is treated where n(x) fluctuates about unity in a compact domain D, and is equal to unity in the region exterior to D. In the Rytov approximation the total field u(x) generated by an incident field ui(x) has the form u(x)∼ui(x)exp φ(x) where φ(x)ui(x)=(1/4π)∫D (eik||x−y||/||x−y||)k2(n2−1) ×ui(y)dτy. It is shown that under suitable conditions on n(x) and restrictions on ui(x), the approximation is a leading term of a convergent expansion holding for all x in D. This is in contrast to previous theory, which treated the Rytov approximation as an asymptotic expansion valid in the forward-scattered direction.
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    URL: http://dx.doi.org/10.1063/1.526867
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  • 19
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    Proof of the Levinson theorem by the Sturm–Liouville theorem (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1995-1999 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Levinson theorem is proved by the Sturm–Liouville theorem in this paper. For the potential ∫10r||V(r)||dr 〈∞,V(r)→b/r2 when r→∞, the modified Levinson theorem is derived as nl=(1/π)δl(0) +(a−l)/2− 1/2 sin2{δl(0)+[(a−l)/2]π}, if a(a+1)≡b+l(l+1)〉 3/4 or a=0. Two examples which violate the Levinson theorem and satisfy the modified Levinson theorem are discussed.
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    URL: http://dx.doi.org/10.1063/1.526869
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  • 20
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    Bilinear phase-plane distribution functions and positivity (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1986-1994 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: There is a theorem of Wigner that states that phase-plane distribution functions involving the state bilinearly and having correct marginals must take negative values for certain states. The purpose of this paper is to support the statement that these phase-plane distribution functions are for hardly any state everywhere non-negative. In particular, it is shown that for certain generalized Wigner distribution functions there are no smooth states (except the Gaussians for the Wigner distribution function itself) whose distribution function is everywhere non-negative. This class of Wigner-type distribution functions contains the Margenau–Hill distribution. Furthermore, the argument used in the proof of Wigner's theorem is augmented to show that under mild conditions one can find for any two states f, g with non-negative distribution functions a linear combination h of f and g whose distribution function takes negative values, unless f and g are proportional.
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    URL: http://dx.doi.org/10.1063/1.526868
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  • 21
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    Invariant decomposition of the retarded electromagnetic field (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2024-2029 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The integral representation of the electromagnetic two-form, defined on Minkowski space-time, is studied from a new point of view. The aim of the paper is to obtain an invariant criteria in order to define the radiative field. This criteria generalizes the well-known structureless charge case. We begin with the curvature two-form, because its field equations incorporate the motion of the sources. The gauge theory methods (connection one-forms) are not suited because their field equations do not incorporate the motion of the sources. We obtain an integral solution of the Maxwell equations in the case of a flow of charges in irrotational motion. This solution induces us to propose a new method of solving the problem of the nature of the retarded radiative field. This method is based on a projection tensor operator which, being local, is suited to being implemented on general relativity. We propose the field equations for the pair {electromagnetic field, projection tensor}. These field equations are an algebraic differential first-order system of one-forms, which verifies automatically the integrability conditions.
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    URL: http://dx.doi.org/10.1063/1.526873
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  • 22
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    Global aspects of shear-free perfect fluids in general relativity (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2009-2017 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In an earlier investigation of the class of shear-free expanding (or contracting) irrotational perfect fluids obeying a barotropic equation of state p=p( μ), and satisfying the field equations of general relativity, it was shown that the space-times form three distinct classes. In one class, the fluid acceleration is zero (i.e., the flow is geodesic), and the space-times are the well-known spatially homogeneous and isotropic Friedmann–Robertson–Walker (FRW) models. In the other two classes, the acceleration is nonzero, and the space-times are spatially anisotropic and are less familiar. One of these classes consists of the spherically symmetric Wyman solutions, whereas models that are plane symmetric, and either spatially or temporally homogeneous, constitute the final class. Analytic forms for these anisotropic space-time metrics were given, although in each case their exact determination would depend upon the solution of a single nonlinear ordinary differential equation, which has not been achieved. The purpose of the present article is to provide a pictorial description of the solutions of these equations, to depict qualitatively similar and distinct subclasses of solution, and hence to discover in some detail all possible global behaviors of the associated space-times. In all cases, it is found that, when the space-time is sufficiently extended, the fluid exhibits unphysical properties. The conclusion is that shear-free expanding (or contracting) relativistic perfect fluids that obey an equation of state p=p( μ) must be FRW, or else must be restricted to "local'' regions, by means of a suitable extension in which at least one of the conditions defining the entire family is relaxed.
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    URL: http://dx.doi.org/10.1063/1.526871
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  • 23
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    Generalized Weyl-type gauge geometry (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2030-2031 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Weyl-type gauge geometry based on gauging by GL(4, R) and presented in an earlier paper is developed from an alternative point of view, which emphasizes independent geometric objects as the building blocks. This approach avoids most of the elaborate calculations of the earlier paper, and thus contributes to an intuitive understanding. The new building blocks, which are the metric and two different affine connections, uniquely determine the tensorial structures of the earlier paper, and vice versa.
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    URL: http://dx.doi.org/10.1063/1.526874
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  • 24
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    Boson approximants for lattice Fermi systems (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2039-2044 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We demonstrate that Bose systems can be used to simulate properties of their Fermi partners in thermal bath, provided the spectral property HB =PHBP +(1−P)HB(1−P), HF =PHBP can be proved in the state space of the Bose system. The approximation accuracy can be made arbitrarily good by varying the (free) coupling parameter λ∈(0,∞), and permits studying of fermionic partition or correlation functions in a finite volume by means of the standard techniques (Bose:path integral, Monte Carlo, etc).
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    URL: http://dx.doi.org/10.1063/1.526876
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  • 25
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    The harmonic mapping character of Rosen's bimetric theory of gravity and the geometry of its harmonic mapping space (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2032-2038 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: After showing that Rosen's bimetric theory of gravity is a harmonic map, the geometry of the ten-dimensional harmonic mapping space (HMS), and of its nine-dimensional symmetric submanifolds, which are the leaves of the codimension one foliation of the HMS, is detailed. Both structures are global affinely symmetric spaces. For each, the metric, connections, and Riemann, Ricci, and scalar curvatures are given. The Killing vectors in each case are also worked out and related to the "conserved quantities'' naturally associated with the harmonic mapping character of the theory. The structure of the Rosen HMS is very much like that determined by the DeWitt metric on the six-dimensional Wheeler superspace of all positive definite three-dimensional metrics. It is clear that a slight modification of the Rosen HMS metric will yield the corresponding metric on the space of all four-dimensional metrics of Lorentz signature. Finally, interesting avenues of further research are indicated, particularly with respect to the structure and comparison of Lagrangian-based gravitational theories which are similar to Einstein's general relativity.
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    URL: http://dx.doi.org/10.1063/1.526875
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  • 26
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    ζ-function method and the evaluation of fermion currents (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2045-2049 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Using the ζ-function method, a prescription for the evaluation of fermion currents in the presence of background fields is given. The method preserves gauge invariance at each step of the computation and yields to a finite answer showing the relevant physical properties for arbitrary background configurations. Examples for n=2,3 dimensions are worked out, emphasizing the connection between preservation of gauge invariance and violation of other symmetries (chiral symmetry for n=2, parity for n=3).
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    Scalar field propagators in anti-de Sitter space-time (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2050-2058 
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    Notes: Simple expressions are found for the retarded, advanced, and Feynman propagators, as well as several other auxiliary invariant functions, for scalar fields of arbitrary mass in anti-de Sitter space-time.
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    Boson basis realization for shell-model fermion problem (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2067-2071 
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    Notes: The boson basis for the fermion shell-model problem has been realized over a representation space Vn(n−1)/2 of the unitary group U(n(n−1)/2). A contraction of this space was found to yield the generator algebra of U(n). Based on this result it is shown that the transformations induced by the Dyson-mapped boson Hamiltonian on the Dyson boson basis are identical to the corresponding transformations by the fermion Hamiltonian on the shell-model basis.
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    Erratum: A novel class of Bessel function integrals [J. Math. Phys. 25, 2933(1984)] (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2082-2082 
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    ISSN: 1089-7658
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    Topics: Mathematics , Physics
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    Application of linked Bäcklund transformations to nonlinear boundary value problems (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 393-395 
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    Topics: Mathematics , Physics
    Notes: A class of nonlinear boundary value problems is reduced to linear canonical form by a combination of Bäcklund transformations.
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    Infinitesimal null isotropy and Robertson–Walker metrics (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 407-410 
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    ISSN: 1089-7658
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    Notes: The concept of infinitesimal null isotropy is defined for a Lorentz manifold, in terms of null sectional curvature (as defined by Harris). It is shown that infinitesimal null isotropy is equivalent to infinitesimal spatial isotropy (as defined by Karcher), and that a null-isotropic space for which null sectional curvature is infinitesimally spatially constant must have a Robertson–Walker metric.
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    Some properties of hyperspherical harmonics (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 396-403 
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    Topics: Mathematics , Physics
    Notes: A general formula is given for the canonical decomposition of a homogeneous polynomial of order λ in m variables into a sum of harmonic polynomials. This formula, which involves successive applications of the generalized Laplace operator, is proved in the Appendix. It is shown that the group-theoretical method for constructing irreducible Cartesian tensors follows from the general formula for canonical decomposition. The relationship between harmonic polynomials and hyperspherical harmonics is discussed, and an addition theorem for hyperspherical harmonics is derived. An expansion of a many-dimensional plane wave in terms of Gegenbauer polynomials and Bessel functions is derived and used to construct bicenter expansions of arbitrary functions in many-dimensional spaces. Finally, a formula is derived for the 3λ coefficients of hyperspherical harmonics. These coefficients give the values of integrals involving the products of three harmonics.
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    The anti-self-dual Coulomb field in Minkowski space-time (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 428-430 
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    Notes: The twistor encoding of the anti-self-dual Coulomb field is given in terms of the space-time connections pulled back to I+ and to I−. This description differs considerably from that of the twistor encoding of transverse or radiation fields, which have been the only fields studied in this fashion to date. A twisted structure results on I+ and a topologically incomputable one on I− and these are identified modulo the null lines intersecting the source world-line.
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    A twistor encoding of Lienard–Wiechert fields in Minkowski space-time (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 431-433 
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    Notes: The twistor encoding of the anti-self-dual Lienard–Wiechert field on Minkowski space-time yields a considerably richer structure than that of the Coulomb field encoding due to the presence of a nonzero radiation field. The combination of advanced and retarded transverse fields together with the longitudinal field and the individual aspects of these fields provides this structure. Higher-order longitudinal moments can be incorporated so that general longitudinal fields can be given a twistor description.
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    Three-dimensional inverse scattering: High-frequency analysis of Newton's Marchenko equation (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 436-439 
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    Topics: Mathematics , Physics
    Notes: We obtain a high-frequency asymptotic expansion of Newton's Marchenko equation for three-dimensional inverse scattering. We find that the inhomogeneous term contains the same high-frequency information as does the Born approximation. We show that recovery of the potential via Newton's Marchenko equation plus the "miracle'' depends on low-frequency information.
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    Semiclassical statistical mechanics of two-dimensional fluid mixture of hard disks (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 495-504 
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    Notes: High-temperature expansions for the density-independent part of the radial distribution function and the first-order density correction to it are obtained for a two-dimensional binary mixture of hard disks. The "excess'' quantum corrections to the second and third virial coefficients and excess free energy are also discussed. It is found that the "excess'' quantum effect depends on the concentration and the diameter radio.
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    Exact temporal evolution for some nonlinear diffusion processes (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 522-527 
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    Notes: Exact solutions to Fokker–Planck equations with nonlinear drift are considered. Applications of these exact solutions for concrete models are studied. We arrive at the conclusion that for certain drifts we obtain divergent moments (and infinite relaxation time) if the diffusion process can be extended without any obstacle to the whole space. But if we introduce a potential barrier that limits the diffusion process, moments converge with a finite relaxation time.
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    Some static solutions in the general scalar-tensor theory (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 532-535 
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    Notes: Exact solutions are found for the static gravitational fields for a matter-free space in the general scalar-tensor theory of Nordtvedt–Barker–Schwinger. The singular behavior of some of the invariants has also been discussed for the solutions in Barker and Schwinger theories.
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    Fermionic couplings in Kaluza–Klein theories (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 536-541 
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    Notes: The totally symmetric and totally antisymmetric direct couplings of fermions in d-dimensional space are investigated. Explicit forms are given for d〈11. A different way of handling the d-dimensional Dirac algebra is also described.
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    A vector model for electroweak interactions (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 542-550 
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    Notes: In this paper we present a vector model for the electroweak interactions. The Cartan map gives an isomorphism between Dirac bispinors and an isotropic class of Yang–Mills vector fields. The isotropic Yang–Mills vector fields Fk =Ek +iHk with k=1,2,3, satisfy the condition that the matrix of scalar invariants (Fj ⋅Fk) equals a scalar multiple of the identity matrix. We show that all the bispinor observables commute with the Cartan isomorphism, including all gauge transformations, as well as Lorentz transformations. We derive the Yang–Mills equivalent Dirac equation. As a consequence of the vector model, we obtain a new Lagrangian for electroweak interactions, which is an alternative to the Weinberg–Salam Lagrangian. Moreover, we show that the vector model predicts that the Weinberg angle θw satisfies sin2 θw =0.25, which is close to the measured value of sin2 θw =0.23. The vector model accommodates all the lepton and quark flavors. Furthermore, it predicts the conservation of baryon number and lepton number, as well as electric charge in electroweak interactions. The vector model also gives a new interpretation to antiparticles. In the vector model, an antiparticle is characterized by its opposite baryon number, lepton number, and electric charge; yet both particles and antiparticles propagate forward in time with positive energies.
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    Morphisms of crystallographic groups: Kernels and images (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 219-228 
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    Notes: The crystallographic groups play an important role in solid state physics, where their representations are of particular interest. In this paper we classify the kernels of all possible representations by deriving necessary and sufficient conditions for a subgroup H of a crystallographic group G to be invariant. The structure of G/H is also discussed. A list of the one- and two-dimensional invariant subgroups of the two-dimensional crystallographic groups is appended as Table I; it includes the structural features of these subgroups needed for determining their settings, relative to the parent groups, and identifies the corresponding images. Table II is a list of the commutator subgroups of the two-dimensional groups.
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    Exact calculation of the lineshape and the scattering operator for a model of a two-level atom interacting with a continuous spectrum of radiation (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 556-565 
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    Notes: In this paper we calculate exactly the lineshape for a model of an excited two-level atom in interaction with a continuous spectrum of radiation for the problem of spontaneous emission. Specifically, for the case of a d=1 radiation field, we use the exact results reported in our earlier work [J. Math. Phys. 14, 414, 423 (1973)] for the probability ρ(τ) of the atom's being in the excited state at time τ to obtain an analytic expression for the lineshape of the emitted radiation (i.e., the photon). We also calculate the lineshape using two Wigner–Weisskopf style approximations and the results, for a given choice of coupling function, are compared numerically with the profile generated using the exact solution. These comparisons show convincingly the success with which these two approximations can be expected to reproduce the qualitative and quantitative features of the exact lineshape for values of the coupling constant α ranging between 0.01 and 0.3. Finally, we calculate explicitly the scattering operator corresponding to the above spontaneous emission problem and work out exactly the probability of forward and backward scattering of a photon by the atom at and away from resonance.
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    An infinite hierarchy of conservation laws and nonlinear superposition principles for self-dual Einstein spaces (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 229-234 
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    Notes: Self-dual Einstein spaces are shown to admit an infinite hierarchy of conservation laws, and this hierarchy is then used to derive a formal version of Penrose's twistor construction. The set of formal holomorphic bundles of fiber dimension 2 over the Riemann sphere P1 is shown to form a formal infinite group which is used to derive nonlinear superposition principles. As an example of our methods a new self-dual Einstein space is obtained as the result of a "collision'' of complex pp-waves "traveling in opposite directions.''
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    Solution of the Cauchy problem for a generalized sine–Gordon equation (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 270-275 
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    Notes: We consider a spectral problem generating a hierarchy of nonlinear evolution equations including the sine-Gordon equation and a physically interesting generalization in the laboratory coordinates. The direct and inverse problems are treated. The time evolution of the spectral data is explicitly given and, therefore, the Cauchy problem for the related equations is solved.
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    Weakly convergent expansions of a plane wave and their use in Fourier integrals (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 276-291 
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    Notes: The Fourier transform of an irreducible spherical tensor is normally computed with the help of the Rayleigh expansion of a plane wave in terms of spherical Bessel functions and spherical harmonics. The angular integrations are then trivial. However, the remaining radial integral containing a spherical Bessel function may be so complicated that the applicability of Fourier transformation is severely restricted. As an alternative, the use of weakly convergent expansions of a plane wave in terms of complete orthonormal sets of functions is suggested. The weakly convergent expansions of a plane wave are constructed in such a way that their application in Fourier integrals leads to expansions of the Fourier or inverse Fourier transform that converge with respect to the norm of either the Hilbert space L2(R3) or the Sobolev space W(1)2(R3). Accordingly, these weakly convergent expansions may be viewed as distributions that are defined on either L2(R3) or W(1)2(R3). The properties of some complete orthonormal sets of functions, in particular their Fourier transforms, are also studied. Shibuya and Wulfman [Proc. R. Soc. London Ser. A 286, 376 (1965)] derived an expansion of a plane wave involving the four-dimensional spherical harmonics. It is shown that this Shibuya–Wulfman expansion is also a distribution which is defined on the Sobolev space W(1)2(R3). Finally, as an application it is shown how weakly convergent expansions can be used profitably for the construction of addition theorems.
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    Lie symmetries of some equations of the Fokker–Planck type (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 3042-3047 
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    Notes: The structure of the local Lie groups of symmetries of some partial differential equations of the Fokker–Planck type in one space dimension is investigated. A connection between these groups and the group SL2(R) is established in the sense that they are all shown to be locally isomorphic to SL2(R)A, where A is the radical. It is conjectured that the groups of Lie symmetries of all Fokker–Planck equations in one space dimension have this structure. The notion of partial invariance, due to Ovsiannikov, is applied to the equations studied. It appears plausible that the class of partially invariant solutions of these equations is larger than the class of invariant solutions although no explicit demonstration of this claim is available at present.
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    The infinite coupling limit of perturbative expansions from a variational extrapolation method (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 3048-3052 
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    Notes: A method for extrapolating perturbative power series to infinity is described. It is a Borel partial resummation stabilized by a variational parameter. Two kinds of series relative to the anharmonic oscillators ||x||k, k〉0, are extrapolated in order to illustrate the effectiveness of the method: the Rayleigh–Schrödinger series, on the one hand, which, after extrapolation, provides the strong coupling expansion of the energy levels, and their lattice expansion, on the other hand, from which is extracted the continuum limit.
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    Integrable Hamiltonian systems with velocity-dependent potentials (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 3070-3079 
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    Notes: The integrability of a two-dimensional Hamiltonian in which the potential depends explicitly on the momenta is investigated. Hamiltonians of this kind are encountered in the description of the motion of a particle in a magnetic field. Two integrable classes of potentials are identified and the second integral of motion is constructed for each of them. The singularity analysis of the equations of motion is also performed, confirming once more the relation between the (weak) Painlevé property and integrability.
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    Exact reduced density matrices for a model problem (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 3105-3108 
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    Notes: The reduced density matrices of arbitrary order for the boson problem of N particles, each attracted harmonically to a central point and interacting with each other harmonically, are analytically calculated.
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    Finite-dimensional representations of the Lie superalgebra sl(1,3) in a Gel'fand–Zetlin basis. I. Typical representations (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1640-1660 
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    Notes: In a series of two papers all finite-dimensional irreducible representations of the special linear Lie superalgebra sl(1,3) are constructed. Explicit formulas for the generators in an orthonormal Gel'fand–Zetlin basis of the even subalgebra gl(3) are given. This paper develops a background for constructing the representations. Expressions for the transformation properties of the basis under the action of the generators are written down within all typical sl(1,3) modules.
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    Transition matrix of point interactions as the scaling limit of integrable potentials on the real line (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1675-1679 
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    Notes: On the real line, the transition matrix corresponding to the nonrelativistic one-particle Hamilton operator for a finite number of zero-range interaction points is the scaling limit of the transition matrix for corresponding integrable potentials.
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    Scattering theory for long-range systems at threshold (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1661-1674 
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    Notes: Scattering theory is discussed for long-range systems around threshold, taking into account explicitly the possibility of zero-energy eigenstates of the underlying Schrödinger Hamiltonian. Low-energy expansions are derived for the scattering amplitude in the different cases. The Coulomb-modified scattering length and effective range parameter are defined directly in terms of the scattering amplitude. Explicit formulas for these quantities are provided. No spherical symmetry of the interaction is assumed.
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    Quantization of systems with many degrees of freedom by the method of collective coordinates: Quantum mechanics around a classical periodic orbit (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1680-1694 
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    Notes: A fairly complete perturbation theoretical solution of the Schrödinger equation around a classical periodic orbit is given as an example demonstrating the quantization of a system with many degrees of freedom by the method of collective coordinates. In particular, explicit expressions are derived for the creation and annihilation operators of quantum fluctuations orthogonal to the classical path, as well as the corresponding eigenfunctions, in both the adiabatic and nonadiabatic domains. It is also shown that corresponding expressions become proportional (and thus can be linked) in domains where they overlap. Finally the splitting of asymptotically degenerate states, and hence the band structure of the resulting spectrum, is calculated.
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    On the relation between gauge theories, moving frames, fiber bundles, and parastatistics (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1695-1700 
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    Notes: We write down standard gauge field theory in a basis-independent manner using the ideas of moving frames (fiber bundles). Then we describe the construction of frames for gauging parafields. To do this (frames) bases for fields are replaced by Clifford matrices. These matrices are in one-to-one correspondence with the number of spinor components. We briefly examine the objects upon which they can act (through matrix multiplication on the left). These objects bear the same relations to spinors that spinors do to vectors. Finally, we show how to construct a set of inner products for the parabases that yield the same action and n-point functions as in the standard field theory.
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    Solution of the Schrödinger equation for a particle in an equilateral triangle (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2784-2786 
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    Notes: The complete solution for the quantum-mechanical problem of a particle in an equilateral triangle is derived. By use of projection operators, eigenfunctions belonging explicitly to each of the irreducible representations of the symmetry group C3V are constructed. The most natural definition of the quantum numbers p and q includes not only integers but also nonintegers of the class (1)/(3) and (2)/(3) modulo 1. Some relevant features relating to symmetry and degeneracy are also discussed.
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    Spectral sum rule for time delay in R2 (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2796-2802 
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    Notes: A local spectral sum rule for nonrelativistic scattering in two dimensions is derived for the potential class v∈L4/3 (R2). The sum rule relates the integral over all scattering energies of the trace of the time-delay operator for a finite region Σ⊆R2 to the contributions in Σ of the pure point and singularly continuous spectra.
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    On the covariance of Dirac's modified canonical commutation relations for fermions interacting with gravity and bosons (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2827-2835 
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    Notes: For fermions in curved space-time, where i(h-dash-bar)ψ° is no longer the canonical conjugate of ψ, canonical quantization according to Dirac requires use of "modified'' graded commutation relations, in which the canonical conjugates to the tetrad field components are no longer commutative with each other or with the fermion field. As shown earlier by the DeWitts, these modified commutation relations may be understood as a canonical quantization of new field variables that can conventionally be interpreted in terms of creation and annihilation operators. Because of the horrible transformation properties of these new variables, covariance of this quantization of fermion fields and of the gravitational field with which the fermions interact is best proved in terms of the old variables. Like canonical quantization, also this modified quantization requires alteration of the theory destroying general invariance of the Lagrangian. As discussed in a preceding paper, covariance of this modified quantization under a group of finite transformations will follow, under the conditions that (1) it can be proved for a generator T1, linear in infinitesimal descriptors of the transformations, that by these modified commutation relations it will generate the substantial variations of the canonical field variables, while (2) the second-order generator T12, constructed from T1 as previously discussed, will be conserved and invariant. It is here proved that these two conditions are satisfied, provided that the transformations leave the Lagrangian function L invariant. This restriction limits the proof of covariance of quantization to affine transformations only. It is discussed why this yet leaves the possibility of general covariance of the "physical part'' of this quantization procedure.
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    Confined gravitational fields produced by anisotropic fluids (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2847-2849 
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    Notes: A family of solutions of the Einstein equations for a spherically symmetric distribution of anisotropic matter is presented, which can be matched with the flat (Minkowskian) space-time on the boundary of the matter, although the energy density and stresses are nonvanishing within the sphere.
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    Collision-free gases in spatially homogeneous space-times (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2869-2880 
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    Notes: The kinematical and dynamical properties of one-component collision-free gases in spatially homogeneous, locally rotationally symmetric (LRS) space-times are analyzed. Following Ray and Zimmerman [Nuovo Cimento B 42, 183 (1977)], it is assumed that the distribution function f of the gas inherits the symmetry of space-time, in order to construct solutions of Liouville's equation. The redundancy of their further assumption that f be based on Killing vector constants of the motion is shown. The Ray and Zimmerman results for Kantowski–Sachs space-time are extended to all spatially homogeneous LRS space-times. It is shown that in all these space-times the kinematic average four-velocity ui can be tilted relative to the homogeneous hypersurfaces. This differs from the perfect fluid case, in which only one space-time admits tilted ui, as shown by King and Ellis [Commun. Math. Phys. 31, 209 (1973)]. As a consequence, it is shown that all space-times admit nonzero acceleration and heat flow, while a subclass admits nonzero vorticity. The stress πij is proportional to the shear σij by virtue of the invariance of the distribution function. The evolution of tilt and the existence of perfect fluid solutions is also discussed.
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    Spacelike conformal Killing vectors and spacelike congruences (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2881-2901 
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    Notes: Necessary and sufficient conditions are derived for space-time to admit a spacelike conformal motion with symmetry vector parallel to a unit spacelike vector field na. These conditions are expressed in terms of the shear and expansion of the spacelike congruence generated by na and in terms of the four-velocity of the observer employed at any given point of the congruence. It is shown that either the expansion or the rotation of this spacelike congruence must vanish if Dna/dp =0, where p denotes arc length measured along the integral curves of na, and also that there exist no proper spacelike homothetic motions with constant expansion. Propagation equations for the projection tensor and the rotation tensor are derived and it is proved that every isometric spacelike congruence is rigid. Fluid space-times are studied in detail. A relation is established between spacelike conformal motions and material curves in the fluid: if a fluid space-time admits a spacelike conformal Killing vector parallel to na and naua =0, where ua is the fluid four-velocity, then the integral curves of na are material curves in an irrotational fluid, while if the fluid vorticity is nonzero, then the integral curves of na are material curves if and only if they are vortex lines. An alternative derivation, based on the theory of spacelike congruences, of some of the results of Collins [J. Math. Phys. 25, 995 (1984)] on conformal Killing vectors parallel to the local vorticity vector in shear-free perfect fluids with zero magnetic Weyl tensor is given. The necessary and sufficient condition for vortex lines to be material lines is derived and the restriction this places on the flow of a thermodynamical perfect fluid is determined. As an application, a pure magnetic field in a rotational fluid is considered and results similar in nature to Ferraro's law of isorotation are obtained. Throughout, corresponding results for a timelike conformal motion and for Newtonian theory are given for comparison.
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    Erratum: New inequalities for the Coulomb T matrix in momentum space [J. Math. Phys. 25, 3033 (1984)] (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 3016-3016 
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    Supertwistor realization of SU(2,2/1) (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1828-1833 
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    Notes: A space of supertwistors is introduced as a graded vector space by starting with ordinary twistor space multiplied with even Grassmann coefficients and combining it by an othogonal direct sum with a one-dimensional space multiplied with odd Grassmann coefficients. A treatment of the algebraic properties of supertwistor space and of Grassmann-linear transformations on this space lead to a systematic procedure for deriving the structure equations for the graded Lie algebra su (2,2/1).
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    Supertwistor fiber bundles as a formalism for supergravities (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1834-1846 
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    Notes: A gauge theory of supergravity which allows one to obtain first-order Lagrangians that are locally gauge invariant by construction is presented. The formalism makes use of supertwistors as a representation space for the construction of a typical fiber of a vector bundle associated with a principal bundle, where the structural group is the super-Poincaré group. The approach proposed provides a means of resolving one of the central problems of gauge field theories of external symmetry groups, that is the satisfactory treatment of translations.
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    Gauge fixing and Gupta–Bleuler triplets in de Sitter QED (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1847-1854 
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    Notes: Binegar et al. recently developed de Sitter QED within the frame of a particular gauge fixing c= (2)/(3) . Such a choice leads to the simplest possible structure of the Gupta–Bleuler triplets, with the SO(3,2) representations D(3,0) and D(1,1) appearing to describe special gauge solutions. The present work examines the general case c≠ (2)/(3) by considering explicitly the corresponding homogeneous propagators and some fundamental carrier states for the related indecomposable representations of SO(3,2). The latter expressions involve "logarithmic'' gauge states which independently carry extensions of the D(3,0) and D(1,1) Lie algebra representations.
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    On a computation formula for the representation matrices of U(n) (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2480-2484 
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    Notes: A d-matrix element of U(n), which is called the semi-highest-weight d-matrix element and plays an essential role for the D-matrix elements, is explicitly determined. By using the result, a formula of computing the D-matrix elements of U(n) is given in terms of lowering operators corresponding to those of Nagel and Moshinsky.
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    Deficiency indices and singular boundary conditions in quantum mechanics (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2520-2528 
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    Notes: We consider Schrödinger operators H in L2(Rn), n ∈ N, with countably infinitely many local singularities of the potential which are separated from each other by a positive distance. It is proved that due to locality each singularity yields a separate contribution to the deficiency index of H. In the special case where the singularities are pointlike and the potential exhibits certain symmetries near these points we give an explicit construction of self-adjoint boundary conditions.
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    On the semiclassical description of N-level systems interacting with radiation fields (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2529-2539 
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    Notes: It is shown that the dynamics of an N-level quantum system driven by a classical radiation field can be derived rigorously from an associated fully quantum-mechanical model with the help of an asymptotic limit. By formally expanding the full quantum dynamics around the semiclassical limit, quantum corrections to the semiclassical description are systematically constructed. The observables describing these corrections are shown to exist in any order, and explicit expressions for their time dependence are given.
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    Spectral properties of the Dirac equation with anomalous magnetic moment (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2556-2559 
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    Notes: Though the electron possesses an anomalous magnetic moment, this term has so far been treated by perturbation methods only. Here this rather singular term is treated nonperturbatively. For a general and large class of spherical potentials it is shown that the Hamiltonian is essentially self-adjoint. If the potentials vanish at infinity the essential spectrum is R(backward-slash)(−m,m). These results hold for all, also strong, Coulomb-type potentials. We further establish that the eigenvalues for such Hamiltonians are stable and can be computed by a low-order perturbation theory, if l≥3. The above results can also be extended to multicenter potentials.
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    Is perturbation theory misleading in general relativity? (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2581-2588 
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    Notes: Two senses in which the perturbation equations of general relativity can be misleading are explored. (i) Under certain circumstances there exist solutions of the perturbation equations that appear to be gauge, in that the metric perturbation is the symmetrized derivative of a vector field, but which nonetheless are not true gauge. (ii) Under certain circumstances there exist solutions of the perturbation equations that cannot, even locally, be extended to higher order in perturbation theory. The latter is a local version of the well-known phenomenon of "linearization instability.''
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    Hopf bifurcation in Yang–Mills mechanics (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2643-2647 
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    Notes: The periodic non-Abelian space-independent solutions to Yang–Mills SU(2) equations are studied. Hopf bifurcation is shown to appear. New analytic solutions generating a simple Abelian source are found and their stability is discussed. The source can be produced by a fermion field; a self-consistent solution of Yang–Mills–Dirac equations is presented.
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    On extensions of supersymmetry algebras in d=4 and 11 (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2659-2665 
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    Notes: SUSY algebras, in d=4 and 11, are analyzed, extended by the addition of both spinorial and bosonic central charge generators. It is found that only limited extensions are possible, on use of Jacobi identities. Casimirs, irreps, and spin reduction are discussed, and the problems of constructing actions for SUSY and supergravity theories as full superspace actions are considered.
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    A general approach to the systematic derivation of SO(3) shift operator relations. I. Theory (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 128-132 
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    Notes: A new technique is established for the construction of relations between products consisting of two, three, or more SO(3) shift operators, within the framework of the Lie algebras of SO(3) tensor operators constructed out of an underlying single-boson structure.
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    Finite hard rod systems and their thermodynamic limit. III. Collision frequency, no-collision probability, and velocity autocorrelation function (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2617-2626 
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    Notes: We use the methods developed for the one-dimensional hard rod gas in the preceding papers to derive exact expressions for the average number of collisions per unit time, the probability that a tagged particle does not collide with other ones within a given time interval, and the velocity autocorrelation function. It is discussed how these expectation values, obtained for finite systems and three kinds of ensembles (smallest stationary, microcanonical, and canonical), behave as the size of the system increases (thermodynamic limit).
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    A local limit theorem for strongly dependent random variables and its application to a chaotic configuration of atoms (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1165-1172 
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    Notes: We investigate one-dimensional chaotic configurations of atoms, which are generated by the Baker transformation or, equivalently, by the Bernoulli shift. The problem of calculating the distribution of the jth nearest-neighbor distances of these configurations is shown to be equivalent to the task of finding the limit distribution of the sum of the strongly dependent random variables Xl:([0,1),μL)→[0,1), x→(2lx)mod 1 (l∈N0, μL is the Lebesgue measure). We prove the validity of a local limit theorem for this sequence of random variables and conclude, therefore, that the distribution density Gj of the jth nearest-neighbor distances is asymptotically (as j→∞) a Gaussian distribution, the width of which grows as (j)1/2. With the aid of this result, we prove that the pair distribution function G of our configurations, which is the sum of the Gj's, tends to unity in the limit of large distances.
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    Generalization of the diffusion equation by using the maximum entropy principle (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1173-1174 
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    Notes: By using the so-called maximum entropy principle in information theory, one derives a generalization of the Fokker–Planck–Kolmogorov equation which applies when the n first transition moments of the process are proportional to Δt, while the other ones can be neglected.
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    On the wave operator in few-body quantum scattering with Coulomb-like interactions (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 139-142 
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    Notes: Functional analytical methods like strong approximation of operator-valued functions and Dunfords' calculus are applied to yield a contour integral representation with a finite contour of wave operators for nonrelativistic potential scattering with Coulomb and short-range interactions, which avoids high singularities of Coulomb-like Green's functions of stationary scattering theory. The Green's function is the unique solution of the resolvent equation, which has an A-proper kernel allowing projector methods for its solution.
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    The short-range expansion for multiple well scattering theory (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 145-151 
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    Notes: We expand the scattering amplitude and the scattering matrix around the zero-range limit, i.e., with point interactions, in the case when the potential has a finite number of wells. The lower-order terms are largely independent of the shape of the potentials.
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    An effective algorithm for obtaining polynomials for dimer statistics. Application of operator technique on the topological index to two- and three-dimensional rectangular and torus lattices (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 157-167 
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    Notes: Recursion formulas on the numbers of ways for placing an arbitrary number of indistinguishable dumbbells on the various rectangular lattice spaces (3×n, 4×n) and torus spaces (2×n, 3×n, 2×2×n) were obtained by the use of the operator technique to the counting polynomial on the topological characteristics (e.g., nonadjacent number, Kekulé number, and topological index). Perfect matching numbers or Kekulé numbers were also obtained for larger lattices such as the 4×n torus and the 2×3×n lattice. By deriving these new results the utility of the proposed method for dimer statistics is demonstrated and some of their mathematical features are discussed.
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    Symmetries of gauge fields (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 192-197 
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    Notes: The concept of homogeneity for a gauge field is introduced as an appropriate geometrical interpretation of the symmetric properties of the gauge field relative to a group of space-time transformations. It is more general than the formulation in terms of an invariant connection, as illustrated by an example on translational symmetries. Sufficient conditions are given for invariance to be equivalent to homogeneity. Both finite and infinitesimal symmetries are treated.
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    Electrodynamics in eight-dimensional space (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 208-210 
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    Notes: Generalized electromagnetic fields and the corresponding generalized electromagnetic field tensor in a real eight-dimensional space-time manifold have been constructed, in terms of which the generalized Maxwell's field equations have been derived. The Lorentz force acting on a charged particle moving in generalized electromagnetic fields has been derived by constructing an eight-velocity vector in this space.
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    Multiplicity-free, unitary and nonunitary irreducible representations of SL(3,R) (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 21-28 
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    Notes: Multiplicity-free, irreducible representations of the group ∼(SL(3,R)) are obtained from SU(2) subgroup representations by a constructive method. It is observed that there exist two series of unitary representations with k contents {k0,k0+1,k0+2,...}k0≥3, {k0,k0+2,k0+4,...} k0=0, 1, 1/2 and finite-dimensional representations with k content {k0+1,k0+3,...,k0+2n+1} k0=1, 1/2 {2,4,6,...,2n}, n=1,2,...,k0=0.
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    Vector fields near caustics (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1404-1407 
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    Notes: The modified Lagrange manifold technique enables determination of the asymptotic series solution of linear scalar wave equations near caustics of simple geometries. Here the technique is extended to include vector field considerations and more complicated caustic geometries.
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    Erratum: Remarks on canonical transformations in phase-space path integrals [J. Math Phys. 24, 874 (l983)] (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1436-1436 
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    Topics: Mathematics , Physics
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    URL: http://dx.doi.org/10.1063/1.526905
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    Lie transformation group solutions of the nonlinear one-dimensional Vlasov equation (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1428-1435 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The solution of the exact, nonlinear one-dimensional Vlasov equation with a space- and time-dependent electric field is reduced to the solution of a nonlinear, first-order ordinary differential equation with two subsidiary equations. The reduction holds for any electric field nonlinear in the spatial coordinate or for a subclass of electric fields linear in the spatial coordinate and is equivalent to the solution of a generalized Bernstein–Greene–Kruskal (BGK) Vlasov equation with a velocity-dependent Lorentz force. The Lie method for the solution of differential equations invariant under a transformation group has been used to calculate the group generator, the canonical variables, and the generalized BGK Vlasov equation. Analytical forms for the functional dependence of the Vlasov equation one-particle distribution function are given.
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    URL: http://dx.doi.org/10.1063/1.526964
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    Dual physical interpretation of the energy tensor: Nonexistence of the Kerr–Newman example (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1021-1023 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Several recent papers have dealt with the possibility of interpreting the Kerr–Newman metric as a viscous fluid as well as its usual interpretation of a rotating, charged black hole. In this paper we show that there is no possible viscous fluid with the Kerr–Newman metric.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526586
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    The relationship between monopole harmonics and spin-weighted spherical harmonics (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1030-1033 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We compare two independent generalizations of the usual spherical harmonics, namely monopole harmonics and spin-weighted spherical harmonics, and make precise the sense in which they can be considered to be the same. By analogy with the spin-gauge language, raising and lowering operators for the monopole index of the monopole harmonics can immediately be written down.
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    URL: http://dx.doi.org/10.1063/1.526533
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    Separability of the Dirac equation in a class of perfect fluid space-times with local rotational symmetry (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1034-1039 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Chandrasekhar's technique for separation of the Dirac equation in the Kerr background is applied to perfect fluid space-times with local rotational symmetry. These space-times fall into three distinct types. It is found that in case (1) the Dirac equation separates if the space-time is at least "locally static'' while in case (3) it separates if the space-time is at least "locally diagonal,'' in contrast to the massless case where Dhurandhar, Vishveshwara, and Cohen showed that the Hertz potential is separable in all cases. In case (2), however, the Dirac equation is separable in all those cases where the Hertz potential for neutrinos is separable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526534
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    Equilibrium states of inhomogeneous mean-field quantum spin systems with random sites (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1049-1056 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For inhomogeneous mean-field quantum spin systems with random sites, we prove that the weak*-limit points of the sequence of n-particle Gibbs states, on a suitable C*-algebra, are superpositions of inhomogeneous product states, which are given by solutions of a generalized Curie–Weiss equation. Under certain conditions there is only one weak*-limit point. As applications, the BCS model and a spin system with cosine interaction are studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526536
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    Proof of the decoupling theorem of field theory in Minkowski space. II. Theories involving particles with vanishingly small masses (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1065-1069 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The decoupling theorem of quantum field theory is studied in Minkowski space for theories which on experimental grounds may contain particles with vanishingly small masses. Rules are set up to prove the distributional vanishing property of the renormalized amplitudes when any subset of the underlying masses is scaled to infinity, and any subset of the remaining masses is scaled to zero. By careful estimates, the analysis in Minkowski space may be reduced to a similar one in Euclidean space. All subtractions of renormalization are carried out at the origin of momentum space with the degree of divergence of a subtraction coinciding with the dimensionality of the corresponding subdiagram.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526538
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    Conformal symmetry and constants of motion (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1072-1076 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Conformal space-time symmetries of electromagnetic fields and potentials are studied in order to determine whole sets of constants of motion when spin- 1/2 charged particles interact with such external electromagnetic fields. The relativistic and nonrelativistic contexts are discussed through the Hamiltonian formalism. In particular, the interesting example of the magnetic monopole field is recovered and related to the recent works of Jackiw and D'Hoker–Vinet.
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    URL: http://dx.doi.org/10.1063/1.526540
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    Lagrangian dynamics on higher-dimensional spaces with applications to Kaluza–Klein theories (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1083-1092 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We review and apply the method of Lagrangian dynamics to particle motion in higher-dimensional spaces. We discuss in detail the case of a Kaluza–Klein theory with coset spaces as fiber. While the total metric we use in general need not allow for Killing vectors, we require that the restriction to the fiber does. We find that for general Jordan–Thiry scalar fields, the geodesic motion in total space is not describable in terms of particle motion in the base manifold with the usual internal charges. The cases when this is possible are discussed. We also consider the geodesic motion in the Sorkin–Gross–Perry Kaluza–Klein monopoles. We find all the conserved quantities and the equations can be integrated by quadrature.
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    URL: http://dx.doi.org/10.1063/1.526542
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    A generalization and refinement of Madivanane's theorem on general involutional transformations (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2087-2091 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A result of Madivanane on "quasianticommuting'' complex square matrices, which are roots of the identity matrix, is generalized to linear operators on infinite-dimensional complex vector spaces. A constant which appears in the result is shown to be nonzero by giving a simple formula for its absolute value. Also, a simple formula for the constant itself is given, which is valid for some cases.
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    URL: http://dx.doi.org/10.1063/1.526831
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    Nontrivial zeros of weight 1 3j and 6j coefficients: Relation to Diophantine equations of equal sums of like powers (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2092-2095 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The nontrivial zeros of weight 1 3j and 6j coefficients given previously are shown to be the set of all such zeros. The relation of these zeros to the solutions of well-known Diophantine equations is also discussed.
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    URL: http://dx.doi.org/10.1063/1.526832
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    Linearization of nonlinear differential equations by means of Cauchy's integral (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 929-939 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is suggested to transform a class of nonlinear differential equations with a holomorphic type of nonlinearity into linear integrodifferential equations. The method is presented in detail for first-order ordinary differential equations. The transformed equation is studied and is found to have a unique solution with an analytical representation. In a numerical test calculation rapid convergence of an approximate solution of the linearized equation towards the reference solution is found. The method can be applied to higher-order ordinary and partial differential equations. The transformation can be generalized also to operator-valued differential equations.
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    URL: http://dx.doi.org/10.1063/1.526549
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    The Hamiltonian structure of a complex version of the Burgers hierarchy (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 943-945 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper we construct a class of integrable Hamiltonian nonlinear evolution equations generated by a purely differential recursion operator. It turns out that this hierarchy is a complex version of the Burgers hierarchy and can be linearized through a generalization of the Cole–Hopf transformation.
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    URL: http://dx.doi.org/10.1063/1.526551
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    Numerical integration in many dimensions. I (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 951-954 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: If a d-dimensional integral involves an integrand of the functional form F( f1(x1)+f2(x2)+⋅⋅⋅), then one can introduce an integral transform (Fourier or Laplace or variants on those) which allows all the integrals over the coordinates xi to factor. Thus a d-dimensional integral is reduced to a one-dimensional integral over the transform variable. This is shown to be a very powerful and practical numerical approach to a number of problems of interest. Among the examples studied is the computation of the volume of phase space for an arbitrary collection of relativistic particles. One important aspect of the approach involves numerical integration along various contours in the complex plane.
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    URL: http://dx.doi.org/10.1063/1.526553
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    A summation method for the Rayleigh–Schrödinger series for the anharmonic oscillator (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 961-964 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We approximate the energy levels of the anharmonic oscillator with any coupling constant by eigenvalues λj( g,T) of the operator −d2/dx2+x2+gVT(x) with VT(x) =x4 when ||x||≤T and VT(x) =T4 when ||x||〉T. The functions λj( g,T) are holomorphic with respect to g in a neighborhood of the non-negative half-axis. The conformal transformation maps this neighborhood onto the unit circle of the complex plane. It gives the summation method for the Rayleigh–Schrödinger series for every g≥0.
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    URL: http://dx.doi.org/10.1063/1.526556
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    Strong approximation of time evolution operators for a finite system of oscillators with nonlinear coupling (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 970-972 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider a system in three space dimensions consisting of a finite number of oscillators with a nonlinear interaction. Using projectors on N-particle subspaces of the Fock space, we show that the time evolution operator is strongly approximatable by exponentials of self-adjoint finite-rank operators (finite-dimensional Hermitian matrices), which can easily be calculated in the corresponding eigenrepresentation.
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    URL: http://dx.doi.org/10.1063/1.526558
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    Branching index sum rules for simple Lie algebras (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2127-2137 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Let L and L0 be a simple Lie algebra and its sub-Lie algebra, respectively. Then, a given irreducible representation ω of L decomposes into a direct sum of irreducible components of L0, which is called the branching rule. The general Dynkin indices introduced earlier satisfy many sum rules for the branching rule. These are found to be strong enough to uniquely determine the branching rule for many cases we have studied. The sum rules are especially useful for cases of exceptional Lie algebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526835
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    Boson realization of sp(4). I. The matrix formulation (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2107-2123 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Holstein and Primakoff derived long ago the boson realization of a su(2) Lie algebra for an arbitrary irreducible representation (irrep) of the SU(2) group. The corresponding result for su(1,1)≅sp(2) is also well known. This raises the question of whether it is possible to obtain in an explicit, analytic, and closed form, and for any integer d, the boson realization of a sp(2d) Lie algebra for an arbitrary irrep of the Sp(2d) group, which is a problem of considerable physical interest. The case d=2 already illustrates the problem in its full generality and thus in this paper we concentrate on sp(4). The Dyson realization is well known, and the passage to bosons satisfying the appropriate Hermiticity conditions can be done by a similarity transformation through an operator K. What we want, though, is an explicit boson realization for sp(2d) similar to the one that exists for sp(2). In Sec. VI we show how we can get it for sp(4) if the operator K is known. Unfortunately while the matrix form of K2 can be explicitly derived from definite recursion relations, the same cannot be said of K as it involves, in general, the solution of algebraic equations of high degree. Thus the conclusion, corroborated also by a classical analysis where K does not appear, is that an explicit, analytic, and closed boson realization of sp(4), and thus also of sp(2d), is only possible for particular irreps of the corresponding groups.
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    URL: http://dx.doi.org/10.1063/1.526833
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