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  • Books  (27)
  • Articles  (13,046)
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  • 1995-1999
  • 1985-1989  (13,073)
  • 1950-1954
  • 1988  (13,073)
  • Mathematics  (13,073)
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  • Books  (27)
  • Articles  (13,046)
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  • 1995-1999
  • 1985-1989  (13,073)
  • 1950-1954
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  • 1
    Electronic Resource
    Electronic Resource
    Conditions for the convolution of two Wigner distributions to be itself a Wigner distribution (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 2036-2041 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The convolution of two Wigner distribution functions (WDF's) is always non-negative, but not always a WDF, as Jagannathan et al. [Phys. Lett. A 120, 161 (1987)] have shown. In this paper conditions are given that are sufficient, and probably necessary, for such a convolution to be a WDF, and a new characterization of Gaussian WDF's is obtained as a by-product.
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    URL: http://dx.doi.org/10.1063/1.527861
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  • 2
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    On the representation of Slater-type densities by Gaussian densities (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1758-1760 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is proved that for arbitrary m, n∈N0 and α〉0, β〉0, there exists an integral representation ||x||m ||y||n exp(−α||x||−β||y||) =∫R+×RKmn(s,t)exp[−(s +it)||x||2−(s−it)||y||2]d(s,t), x,y∈R3, where Kmn(s,t) is a singular distribution in D' (R)⊗Z'(R).
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    URL: http://dx.doi.org/10.1063/1.527874
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  • 3
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    Nonperturbative solutions of nonlinear differential equations using continued fractions (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1761-1770 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new approach to the solution of nonlinear differential equations of mathematical physics is presented. Continued fractions are exploited to convert a power series of a solution into a closed form expression that yields an excellent approximation to the exact solution. These solutions contain the appropriate number of arbitrary constants to accommodate boundary conditions. The method is also shown to be capable of generating certain exact solutions. Evidence is provided for the conjecture that the known exact solutions are members of families of exact solutions.
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    URL: http://dx.doi.org/10.1063/1.527875
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  • 4
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    Solutions of reaction-diffusion integral equations describing explosive evolution of densities for localized structures (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1776-1779 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Reaction-diffusion integral equations are studied with special regard to explosive-type solutions. Certain localized structures can grow explosively in time without change in spatial structure. The characteristic shapes can be described in terms of elliptic functions.
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    URL: http://dx.doi.org/10.1063/1.527877
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  • 5
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    Solutions of the wave equations with boundary conditions on the hyperplane z−ct=0 (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1771-1775 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The boundary value problem for the wave equation is discussed with data cursive-phi(r) on the hyperplane z−ct=0. We give the general form of the solution when cursive-phi(r) is an entire function of r2 of order 1 and type 0〈τ〈∞. As a particular case the focus wave mode solutions of the wave equation are obtained.
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    URL: http://dx.doi.org/10.1063/1.527876
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  • 6
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    Introducing division by an "a'' number and a new "b'' number in particle physics (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1780-1785 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper a new "b'' number (b=a1a2⋅⋅⋅an, where n is even and each a is an anticommutative number or Grassmann number) is introduced, and the specialities of this "b'' number are also expounded. Moreover, division by an "a'' number is defined. At the same time a derivative concept of the functional containing an "a'' number is also given in the traditional approach, and a new formula for the derivative of this functional is advanced. The new formula not only encompasses Berezin's formula but also solves the problems that cannot be solved by Berezin's formula. For "b'' numbers, a unique infinitesimal calculus will be proposed.
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    URL: http://dx.doi.org/10.1063/1.527878
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  • 7
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    Global anomalies and algebraic topology (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1795-1806 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The algebraic topology aspect of the global pure gauge anomaly calculation is investigated. In particular, the use of a cohomology sequence clarifies the method initiated by Witten [Nucl. Phys. 223, 422, 433 (1983)] and Elitzur and Nair [Nucl. Phys. B 243, 205 (1984)]. Examples in SU(N), Sp(N), and SO(N) are discussed.
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    URL: http://dx.doi.org/10.1063/1.527881
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  • 8
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    The existence of regular partially future asymptotically predictable space-times (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1786-1788 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new definition of asymptotically flat space-times is proposed. It is shown that singularities in these new space-times arise from regular initial data. This leads to a simplification of the assumptions of the cosmic censorship theorem recently proved by the author [Class. Quantum Gravit. 3, 267 (1986)]. It is also shown that in the new asymptotically flat space-times a stronger censorship theorem than that proved so far by the author holds.
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    URL: http://dx.doi.org/10.1063/1.527879
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  • 9
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    Cohomology of the structure sheaf of real and complex supermanifolds (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1789-1794 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The cohomology of the structure sheaf of real and complex supermanifolds is studied. It is found to be nontrivial (also in the real case), unless the supermanifold is De Witt, i.e., it is a fiber bundle on an ordinary manifold with a vector fiber. As a consequence, the Dolbeault theorem can be extended only to complex De Witt supermanifolds. The relevance of the nontrivial cohomology of the structure sheaf to the classification of complex line superbundles is discussed. The relationship between the Picard group of a complex De Witt supermanifold and the Picard group of its body is shown.
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    URL: http://dx.doi.org/10.1063/1.527880
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  • 10
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    Maximal subalgebra associated with a first integral of a system possessing sl(3,R) algebra (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1807-1813 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Conventionally the symmetries of a dynamical system are used to determine the first integrals associated with the system. In this paper the reverse procedure is adopted for one-dimensional systems possessing SL(3,R) symmetry. The equivalence of such systems enables the free particle equation to be used as a vehicle. It is observed that for three particular first integrals, each gives rise to a triplet of generators having isomorphic algebras. It is then shown how the knowledge of a first integral and its associated triplet enables one to obtain the remaining integrals and triplets.
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    URL: http://dx.doi.org/10.1063/1.527882
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  • 11
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    Detailed behavior of the phase-integral approximations at zeros and singularities of the square of the base function (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1814-1823 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Approximate solutions to the one-dimensional time independent wave equation, called the phase-integral approximations, are analyzed in the vicinity of characteristic points. The approximations are of arbitrary order and are generated from an unspecified base function. The general theory is illustrated by examples involving the power and/or the exponential behavior of the square of the base function. In these cases simple estimates are derived for the integrals which define the accuracy of the phase-integral approximation, and the optimum approximation order is determined.
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    URL: http://dx.doi.org/10.1063/1.527883
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  • 12
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    Relativistic Schrödinger equations (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1840-1846 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A representation of the Poincaré group by means of operators acting on the function space of the nonrelativistic quantum mechanics is introduced. The conditions that the Hamiltonian of an interacting particle system must verify in order to define a relativistic invariant Schrödinger equation are found out. The relation with usual quantum constraint theories is also studied.
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    URL: http://dx.doi.org/10.1063/1.528188
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  • 13
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    Generalized exponential, circular, and hyperbolic functions for nonlinear wave equations (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1847-1853 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Wave functions are presented in the form of generalized exponentials that are solutions of some of the most usual linear and nonlinear wave equations. The solutions are given in terms of the elliptic functions of Jacobi and presented in a form as similar as possible to the usual circular functions. Some simple theorems are demonstrated to present the solutions as the simplest possible extension of the usual exponentials.
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    URL: http://dx.doi.org/10.1063/1.527887
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  • 14
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    The Heisenberg–Weyl group in the coherent state basis and the Bargmann transform (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1854-1859 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the representation matrices of the quantum mechanical group in the coherent state basis can be used as bases for the expansion of arbitrary square integrable functions on the group. Although this basis is nonorthogonal the expansion can be inverted in a manner similar to an orthogonal basis. Next a coherent state "wave function'' is defined in analogy with the Schrödinger wave function and the above matrix elements are used to determine the action of the group in the space of the coherent state wave functions. The function space in this realization is Bargmann's Hilbert space of analytic functions. It is shown that the mixed basis matrix element between the coordinate and coherent state bases is essentially the integral kernel of Bargmann. The transpose of this matrix element yields the kernel for the inversion of the transform. In this construction the Bargmann transform appears as the unitary transformation connecting the Schrödinger and coherent state wave functions. This considerably simplifies Bargmann's original arguments and yields the integral transform as well as its inversion formula in a simple way.
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    URL: http://dx.doi.org/10.1063/1.527888
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  • 15
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    SU(2) classification of N=2 complex supersymmetric representations (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1949-1957 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The N=2 extended complex supersymmetry representations are constructed. The classification of N=2 multiplets in SU(2) representations is obtained. The relation with N=2 harmonic superspace is also discussed.
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    URL: http://dx.doi.org/10.1063/1.527848
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  • 16
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    The Cauchy problem for stringy gravity (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1891-1895 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Cauchy problem and the propagation of discontinuities for stringy gravity—that is, equations with Gauss–Bonnet terms—in arbitrary dimensions are studied.
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    URL: http://dx.doi.org/10.1063/1.527841
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  • 17
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    Gauge group cohomology in the monopole sector of Yang–Mills theories (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1909-1915 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The theory of Chern–Simons secondary characteristic classes is used to study the gauge group cohomology associated with Yang–Mills theories in sectors with persistent boundary effects. A generalized "descent'' tower of globally defined cocycles (for manifolds with boundaries) is adopted and its relevance to monopole physics is investigated by means of the Christ–Jackiw interpretation for Yang–Mills dyons. In particular, it is found that three-cocycles can arise in the monopole sector of gauge theories and explicit formulas are derived for their description.
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    URL: http://dx.doi.org/10.1063/1.527844
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  • 18
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    Free bosonic string field theory without supplementary fields (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1916-1929 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A covariant local action for free bosonic string fields is constructed without the use of supplementary fields. The open string case is treated in detail. Up to a mathematical conjecture that is likely to hold it is shown that the Virasoro constraints arise as a special choice of gauge. The kinetic operator turns out to be extremely simple, the gauge transformation law arising rather implicitly. The case of closed strings is briefly discussed.
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  • 19
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    Self-energy operator for an electron in an external Coulomb potential. II (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1930-1936 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Relativistic Coulomb Sturmian matrix elements of the operator O≡ln(1−ρ)/ρ, ρ=−[π⋅(1+iσ)⋅π]/m2, in terms of which the self-energy operator for an electron in an external Coulomb potential has been expressed, are studied. The operator O is dealt with on a term by term basis in a Sturmian expansion. Each term of the Sturmian expansion is separated into a part whose matrix elements are analytic functions of Zα, plus a remainder evaluated in closed form by use of the Cauchy residue theorem. All ignorance about the matrix element of the general term in the Sturmian expansion of O is thereby placed entirely in the analytic part, for which an explicit integral representation is derived.
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  • 20
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    On the monotonic dependence of atomic excitation energies on the nuclear charge parameter Z (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1937-1942 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The dependence of atomic excitation energies, i.e., differences of two energy levels, on the nuclear charge parameter Z is examined. For various transitions of heliumlike atoms the associated excitation energies are shown to be monotonic functions of Z. These results and physical arguments suggest the conjecture that such a monotony is a general fact in the nonrelativistic Schrödinger theory of atoms. The proofs given here use upper and lower energy bounds that for two-electron systems are available as explicit expressions in closed form.
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    URL: http://dx.doi.org/10.1063/1.527847
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  • 21
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    A remark concerning canonical commutation relations (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1535-1536 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An elementary quantum mechanical example of canonical commutation relations not equivalent to the Schrödinger representation is discussed. It demonstrates that the "Nelson phenomenon'' occurs in a natural situation.
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    URL: http://dx.doi.org/10.1063/1.527899
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  • 22
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    Multivariable continuous Hahn polynomials (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1529-1534 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A multivariable generalization of the continuous Hahn polynomials is presented; it is a (4p+4)-parameter family, where p is the number of variables. It is shown that they are orthogonal with respect to subspaces of equal degree and biorthogonal within a given subspace. In the simplest case the multivariable weight function takes the form sech[π(x1+x2+⋅⋅⋅+xp)]sech(πx1) sech(πx2)⋅⋅⋅sech(πxp).
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    URL: http://dx.doi.org/10.1063/1.527898
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  • 23
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    Simple orthogonal and unitary compact quantum systems and the I(overdot)nönü–Wigner contraction (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1521-1528 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Compact quantum dynamics, based on the Lie algebra so(n), is known to be relevant to the description of the internal motion of the electron and neutrino. It is shown here that a compact dynamics can also be based on u(n). In both cases there exists a contraction to a noncompact algebra containing a Weyl–Heisenberg subalgebra and consequently, there also exists an approximation scheme defined entirely by the contraction process, in which a sequence of compact systems described in terms of finite square matrices of increasing size, approaches a noncompact system of the usual type, described in terms of operators on a Hilbert space. Particular boson realizations of so(n) and u(n) are shown to be especially convenient for the discussion of the contractions. Some simple illustrative examples of compact systems are treated algebraically and numerically in order to show how their properties approach those of the corresponding noncompact systems.
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  • 24
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    Elliptical billiards and Poncelet's theorem (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1537-1550 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Two- and three-dimensional billiard systems with elliptical and ellipsoidal boundaries, respectively, are studied. It is known that the trajectory of such a two-dimensional system generates a caustic conic curve. Many properties of the elliptical billiard system in the language of projective geometry can be described. One of these properties is that if a trajectory is closed after p bounces, then all trajectories sharing the same caustic conic are also closed after p bounces. In projective geometry, this is known as Poncelet's theorem. Many of the two-dimensional results are extended to three dimensions. In particular, it is shown that all straight segments of a trajectory in a three-dimensional ellipsoidal billiard system are always tangent to two caustic quadrics. If a trajectory is closed after p bounces, then all trajectories sharing the same two caustic quadrics are also closed after p bounces. A generalized Poncelet's theorem in three dimensions is thus established. On the basis of numerical studies, it is conjectured that this generalized Poncelet's theorem is also valid for an arbitrary finite number field. The implications of the results are discussed and their extension to n dimensions is outlined.
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    Alternative Lagrangians for spherically symmetric potentials (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1551-1554 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new, geometrical account of the existence of alternative (s-equivalent) Lagrangians is given for a particle moving in three-dimensional Euclidean space under the influence of a central force. The fact that the Lagrangian for this familiar problem is not unique was pointed out by Henneaux and Shepley [J. Math. Phys. 23, 2101 (1982)]: the present analysis makes the reasons for the phenomenon more transparent than theirs.
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    URL: http://dx.doi.org/10.1063/1.527901
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    N=2 supertori and their representation as algebraic curves (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1555-1568 
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    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: N=2 supertori (N=2 super-Riemann surfaces of genus 1) are classified according to their superconformal equivalence classes. A detailed description of the corresponding supermoduli space is based on this classification. Superelliptic functions are constructed and used for representing the supertori as algebraic varieties in projective superspace. The boundary of N=2, genus 1 supermoduli space is discussed.
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    URL: http://dx.doi.org/10.1063/1.527902
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  • 27
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    Curvature of generic space-times in general relativity (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1569-1574 
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    Topics: Mathematics , Physics
    Notes: Transversality theory is used to study the curvature of generic space-times in general relativity and some applications to unique determination of the metric by the curvature are given.
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  • 28
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    GH∞ supermanifolds (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1575-1579 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: GH∞ -de Witt supermanifolds were recently introduced by Rogers [Commun. Math. Phys. 105, 375 (1986)]. It is shown that these supermanifolds correspond to objects in a specified category of extended graded manifolds (subject only to the condition L〉2q), and some conclusions are drawn about their structure. In particular, it is shown that a GH∞ -de Witt supermanifold is always a vector bundle over its body. Finally it is shown that extended graded manifolds are always trivial extensions of ordinary graded manifolds. This means that all GH∞-de Witt supermanifolds are in fact H∞.
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  • 29
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    Invariants for the time-dependent harmonic oscillator (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1580-1587 
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    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: A systematic method is presented for the construction of invariants for the damped oscillator under the action of a driving force and for the N-dimensional isotropic or anisotropic oscillator. Invariants for time-dependent oscillators are obtained by canonical transformation. The treatment holds in both classical and quantum mechanics.
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    URL: http://dx.doi.org/10.1063/1.527905
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    On the quantization of constrained generalized dynamics (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1588-1592 
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    Notes: A special class of degenerate second-order Lagrangians, those that differ from a nondegenerate first-order Lagrangian by a total time derivative (or a four-divergence) of a function of both the coordinates and velocities, is studied in detail. Using Dirac's theory of constrained systems, it is shown that the canonical quantization starting from the second-order Lagrangian leads to the same physical results as those obtained from the nondegenerate first-order Lagrangian. Then some incorrect results and misleading arguments encountered in the literature on the subject are clarified.
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    Recursion operator and bi-Hamiltonian structure for integrable multidimensional lattices (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1593-1603 
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    Notes: The recursion operator and the bi-Hamiltonian structure for an integrable two-dimensional version of the Toda chain are algorithmically derived from the corresponding linear problem. The intimate relation between two-dimensional theories and non-Abelian one-dimensional theories is emphasized. The analogies and differences between discrete and continuous integrable two-dimensional systems are pointed out and discussed.
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    Application of the Hamilton–Jacobi method to linear nonconservative vibration theory (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1604-1609 
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    Notes: In this paper it is shown how linear, strictly nonconservative, oscillatory systems with one and many degrees of freedom may be analyzed by application of the theory of Hamilton and Jacobi.
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    Hamiltonian structures for systems of hyperbolic conservation laws (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1610-1619 
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    Notes: The bi-Hamiltonian structure for a large class of one-dimensional hyberbolic systems of conservation laws in two field variables, including the equations of gas dynamics, shallow water waves, one-dimensional elastic media, and the Born–Infeld equation from nonlinear electrodynamics, is exhibited. For polytropic gas dynamics, these results lead to a quadri-Hamiltonian structure. New higher-order entropy-flux pairs (conservation laws) and higher-order symmetries are exhibited.
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    The scalar product in two-particle relativistic quantum mechanics (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1620-1633 
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    Notes: In the framework of two-particle relativistic quantum mechanics, a Poincaré-invariant scalar product and the corresponding physical Hilbert space of states are constructed. This is achieved by finding a tensor current of rank 2, jμν(x1,x2), satisfying two independent conservation laws, relative to particles 1 and 2, respectively. Then the scalar product is obtained by integrating the current jμν over two three-dimensional spacelike hypersurfaces. The Hermiticity of the Poincaré group generators is ensured by the fact that the kernel of the current jμν is translation invariant and covariant. A simple expression of the scalar product is obtained when one chooses for the two spacelike hypersurfaces two constant parallel hyperplanes. The positivity of the norm is, in general, ensured if the spectrum of the eigenvalues of the total mass squared operator comes out to be positive.
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    Nonlocal symmetries and the linearization of the massless Thirring and the Federbush models (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1050-1053 
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    Notes: Multilation of nonlocal symmetries of the massless Thirring and the Federbush models leads to transformations linearizing these equations.
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    Conservation laws for nonlinear evolution equations (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1044-1049 
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    Notes: A method to derive conservation laws for evolution equations that describe pseudospherical surfaces is introduced based on a geometrical property of these surfaces. A new third-order evolution equation is obtained as a first example for a nongeneric case in the classification given by Chern and Tenenblat [Stud. Appl. Math. 74, 1 (1986)].
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    On the Gribov ambiguity in the Polyakov string (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1034-1043 
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    Notes: The global aspects of the gauge fixing in the Polyakov path integral for the bosonic string are considered within the Ebin–Fischer–Mareden approach to the geometry of spaces of Riemannian metrics and conformal structures. It is shown that for surfaces of higher genus, the existence of local conformal gauges is sufficient to derive the globally defined integral over the Teichmüller space. The generalized Faddeev–Popov procedure for incomplete gauges is formulated and used to derive the global expression for the Polyakov path integral in the cases of torus and sphere. The Gribov ambiguity in the functional integral over surfaces without boundary can be successfully overcome for arbitrary genus.
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    All possible local charges in a local quantum field theory: Massive case (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1054-1060 
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    Notes: A proof for local charges of the classical result first put forward by Coleman and Mandula [Phys. Rev. 159, 1251 (1967)] is given. Local charges are operators defined as integrals of the time component of conserved Hermitian density currents; in interacting theories they happen to be generators of symmetries of the S matrix.
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    Anomaly coefficients: Their calculation and congruences (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 727-741 
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    Notes: A new method for the calculation of anomaly coefficients is presented. For su(n) some explicit and general expressions are given for these. In particular, certain congruences are discovered and investigated among the leading anomaly coefficients. As an application of these congruences, the absence of global six-dimensional gauge anomalies is shown.
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    The matrix representations of g2. I. Representations in an so(4) basis (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 758-766 
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    Notes: Irreducible representations of the real compact Lie algebra g2 are given in g2&supuline;so(4) bases. All missing labels are accounted for by the explicit construction of a g2&supuline;so(4) basis of vector holomorphic functions. The general problem of missing internal labels is also briefly discussed.
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    Second-degree kinematical constraints associated with dynamical symmetries (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 742-757 
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    Notes: The tensor operators that transform under subrepresentations of the symmetrized Kronecker square of the adjoint representation for the classical semisimple Lie algebras have been determined. All irreducible representations that satisfy the identities obtained by the vanishing of these tensor operators have been deduced. The pairs of irreducible representations of nonexceptional semisimple Lie algebras, the Kronecker product of which decomposes into two irreducible components, have been pointed out. As a consequence of this result, a comparison of the identities, derived in the way indicated before, with those resulting by the application of a method due to Hannabuss, Kostant, and Okubo, has been obtained. Connections between these results and those obtained by Drinfeld, concerning the solutions of quantum Yang–Baxter equations, have been established.
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    The matrix representations of g2. II. Representations in an su(3) basis (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 767-776 
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    Notes: Irreducible representations of the real compact Lie algebra g2 are given in g2&supuline; su(3) bases. A missing label is accounted for by the explicit construction of a g2&supuline; su(3) basis of vector holomorphic functions. Analytical results are given for two multiplicity-free classes of irreps. It is also shown how vector coherent state (VCS) theory accommodates the decomposition of the nilpotent raising operator subalgebra of an arbitrary Lie algebra into a finite but arbitrary number of irreducible tensorial sets under transformations generated by a stability algebra.
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    Theory for correlation functions of fermion quantum fluids (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1678-1686 
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    Notes: A theory for the pair correlation function of a fermion fluid is developed in terms of a function S(m) defined as a certain sum over graphs. The theory is further extended to derive expressions for the radial distribution function and for the four distinct direct correlation functions. These four direct correlation functions are combined together leading to an integral equation for fermion quantum fluids, which is much simpler and is expressed in a computationally convenient form.
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    Superalgebras with Grassman-algebra-valued structure constants from superfields (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 797-801 
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    Notes: Generalized Lie algebras and superalgebras with generators and structure constants taking values in a Grassmann algebra are introduced. Such algebraic structures describe the equal time algebras in the superfield formalism. As an example, the equal time commutators and anticommutators among bilinears made out of the D=1 quantum superfields describing the supersymmetric harmonic oscillator are considered.
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    On the spectrum of a third-order SO(3) scalar in the enveloping algebra of SO(6) (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 802-805 
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    Notes: With the aid of previously derived expressions for the SO(3) reduced matrix elements of the SO(6) generators, which were obtained by considering an intermediate SO(6)↓SU(2)⊗SU(2) reduction, a method is set up to evaluate analytic expressions for the eigenvalues of a third-order scalar operator belonging to the integrity basis of SO(3) scalar operators in the enveloping algebra of SO(6).
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    New classes of symmetries for partial differential equations (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 806-811 
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    Notes: New classes of symmetries for partial differential equations are introduced. By writing a given partial differential equation S in a conserved form, a related system T with potentials as additional dependent variables is obtained. The Lie group of point transformations admitted by T induces a symmetry group of S. New symmetries may be obtained for S that are neither point nor Lie–Bäcklund symmetries. They are determined by a completely algorithmic procedure. Significant new symmetries are found for the wave equation with a variable wave speed and the nonlinear diffusion equation.
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    Unitary highest weight representations of noncompact supergroups (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1275-1282 
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    Notes: The oscillator method for the construction of unitary highest (or lowest) weight representations of noncompact groups and supergroups is generalized. Within this generalization, the method yields unitary highest weight representations of all simple supergroups whose even subgroups are in the form of a direct product of a compact group with a simple noncompact group. The method is illustrated by studying in detail the unitary highest weight representations of the supergroup OSp (2n+1/2m,R). The generalized supercoherent states associated with these unitary representations are also defined.
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    Gell-Mann formula for simple complex Lie groups and geometric quantization (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1300-1307 
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    Notes: A Lie–Poisson isomorphism for Lie algebras @Fg and @Fq=@Fk×@Fk is derived in a closed form, where @Fg is complex and simple, and @Fk is the maximal compact subalgebra in @Fg. This isomorphism enables one to find a generalized Gell-Mann formula relating unitary irreducible representations of the corresponding Lie groups G and Q. The case @Fg=sl(n,C), @Fk=su(n) is considered in detail. A simple relation between characters is obtained.
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    A Grassmann calculus for infinite spin groups (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1283-1299 
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    Notes: The correlation functions of the two-dimensional Ising model satisfy nonlinear equations both on the lattice (discovered by McCoy and Wu [Nucl. Phys. B 180, 89 (1981)] and Perk [Phys. Lett. A1 79, 3 (1980)]) and in a continuum limit (discovered by Wu, McCoy, Tracy, and Barouch and generalized by Sato, Miwa, and Jimbo [Publ. RIMS 14, 223 (1978)]). In this paper results are presented for infinite spin groups that extend results of Sato, Miwa, and Jimbo [Publ. RIMS 14, 223 (1978)] and lead to normal ordered product formulas for the difference of adjacent Ising spin fields. These product formulas are shown to lead directly to the lattice difference equations for the correlations and are also a key ingredient in the scaling limit analysis.
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    τ functions and zero curvature equations of Toda–AKNS type (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1308-1320 
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    Notes: The connection between τ functions and zero curvature equations for the homogeneous construction of the basic module L(Λ0) over the simplest affine Kac–Moody algebra A(1)1 is studied.
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    Integral equations with symmetrical kernel applied to a system with a Dirac-type spectrum (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1321-1324 
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    Notes: The generalized Sturm–Liouville problem for a system with a Dirac-type spectrum was converted to that of a linear integral operator with a symmetrical kernel by Yang [Commun. Math. Phys. 112, 205 (1987)]. A supplementary case is discussed in this paper.
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    Interference in the radiation of two relativistic charges (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1356-1360 
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    Notes: The radiation produced by two interacting relativistic point charges is considered. Under an appropriate approximation the radiation of the system as a whole (interference effects included) is expressed as a function of the relative velocity.
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    Generalized eigenfunction expansions for scattering in inhomogeneous three-dimensional media (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1347-1355 
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    Notes: An infinite number of ways are developed for representing a function in terms of the (generalized) eigenfunctions of a three-dimensional scattering problem and simple known auxiliary functions. The freedom represented by this variety of expansions arises from the causal nature of the wave equations considered. The new expansions are shown to generalize both the Fourier and Radon transforms. An application of the new expansions to the inverse scattering problem is given. It is shown (under some restrictions) that the scattering amplitude and potential are related via one of the generalized transforms.
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    A geometric setting for the quantum planar n-body system, and a U(n−1) basis for the internal states (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1325-1337 
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    Notes: In a previous paper [J. Math. Phys. 28, 964 (1987)], the author showed that the internal motion of a molecule, a many-body system in the Born–Oppenheimer approximation, can be well described in terms of the gauge theory or of the connection theory in differential geometry. However, the scope of that paper centers on the planar triatomic molecule in order to put forward the gauge theory in an explicit manner. This paper is a continuation of the previous one and gives the generalization to the planar multiatomic molecule. The internal space of the n-atomic molecule proves to be diffeomorphic to R+×CPn−2, the product of the positive real numbers and the complex projective space. The internal states of the molecule are described as cross sections in complex line bundles over the internal space. Introduction of the complex line bundles is a geometric consequence of the angular momentum conservation law, because cross sections in each complex line bundle are in one-to-one correspondence with eigenstates that have a fixed total angular momentum eigenvalue. The internal Hamiltonian operator is obtained, which acts on the cross sections in the complex line bundle. Further, boson calculus is performed to obtain a complete basis of internal states of the molecule, using the harmonic oscillator annihilation and creation operators. As a result, carrier spaces of unitary irreducible representations of the unitary group U(n−1), which are characterized by two integers, are realized as finite-dimensional subspaces of the space of the square integrable cross sections in the complex line bundle.
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    When is a Hamiltonian system separable? (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1338-1346 
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    Notes: The Hamiltonian system given by H= 1/2 p2+V(q) with V∈C∞(Rn) is considered. A method for integrating such a system is that of separating the variables in the Hamilton–Jacobi equation. It is known that if such a separation is possible, then it can take place only when the equation is expressed in terms of generalized elliptic coordinates or in a degeneration of these. A criterion is proposed for deciding if separation is possible, and if it is, in which degeneration of elliptic coordinates it takes place.
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    Four-momentum and angular momentum in classical electrodynamics (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1361-1367 
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    Notes: The total four-momentum Pμ and the total angular momentum tensor Mλμ for a classical point charged particle and its field are considered. The standard definition of Pμ and Mλμ is used as the integrals of their respective densities over a spacelike hyperplane orthogonal to the four-velocity of the particle. It is shown that the integral defining Pμ exists and is a conserved quantity, but that the integral defining Mλμ does not exist. The last result is due to the asymptotic behavior of the Coulomb field at spatial infinity.
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    A relativistic quantum mechanical harmonic oscillator without space-time variables (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1389-1395 
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    Notes: Solutions of a linear harmonic oscillatorlike second-order differential equation in a set of complex variables are investigated. This equation has an invariance group homomorphic to the inhomogeneous Lorentz group, IG14. Because of this, it has solutions with particlelike properties—mass, energy, momentum, and spin. These results are interesting for an equation without space-time variables.
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    On a time-dependent extension of the Morse potential (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1396-1404 
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    Notes: A time-dependent extension of a Morse potential is formulated. Both the bound and unbound state wave functions are obtained algebraically for the resulting time-dependent Schrödinger equations, based upon the representations of su(2) and su(1,1), respectively. The method of R-separation of variables is instrumental in the analysis.
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    Coefficients of fractional parentage in the L–S coupling scheme (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1368-1388 
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    Notes: An efficient procedure for the evaluation of the coefficients of fractional parentage (cfp's) for L–S coupled wave functions is presented. The cfp's are calculated separately for N particles, each with angular momentum l (s), coupled into a total angular momentum L (S). The N-particle states formed can belong to any permutational symmetry. The procedure for the evaluation of the L and the S cfp's for arbitrary permutational symmetry is a generalization of the procedure proposed by Bayman and Lande [Nucl. Phys. 77, 1 (1966)] for symmetric and antisymmetric states. It involves the construction and diagonalization of the matrices representing the quadratic Casimir operators for the appropriate special unitary and symplectic (or orthogonal) groups. The cfp's of the antisymmetric L–S coupled states are obtained in terms of products of cfp's for L and S corresponding to conjugate representations of the symmetric group. This method is demonstrated to provide cfp's for L–S states for systems with a considerably larger number of particles than is feasible using the procedures heretofore available.
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    Space-group theory for a nonperiodic icosahedral quasilattice (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 516-524 
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    Notes: The hypercubic lattice Y is considered in Euclidean space E6. Embedding of the icosahedral group A(5) determines a well-known noncrystallographic action of A(5) on an irreducible subspace E3. From boundaries of Y and its metrical dual Y*, new convex polytopes, called Klötze, are constructed in E6. The Klötze tile E6 periodically, but not face-to-face, and provide a new fundamental domain under the hypercubic translation group. All boundaries of a Klotz are parallel or perpendicular to the subspace E3. The intersection of the lattice Y with E3 determine a nonperiodic, face-to-face rhombohedral tiling of E3. A quasicrystal model is introduced in E6 and E3. The model has stable density supported on the rhombohedral tiles. Its Fourier transform yields sharp diffraction maxima and reduces to integrals in E3 over the representative tiles and their boundaries.
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    Projector bases and algebraic spinors (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 2519-2522 
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    Notes: In the case of complex Clifford algebras a basis is constructed whose elements satisfy projector relations. The relations are sufficient conditions for the elements to span minimal ideals and hence to define algebraic spinors.
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    SU(1,1), its connections with SU(2), and the vector model (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 2523-2532 
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    Notes: A relation between representation functions (RF's) of positive discrete unitary irreducible representations (UIR's) of SU(1,1) and the RF's of the UIR's of SU(2) is given. The classical vector model is worked out for the positive discrete UIR's of SU(1,1). Classical domains, probability densities, and algorithms for numerical computations of SU(1,1) RF's and Clebsch–Gordan coefficients are derived, in full analogy with the SU(2) case.
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    On the power-series construction of bound states. I. The energies as zeros of the infinite Hill determinants (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1433-1439 
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    Notes: For a broad class of potentials, we show that the nonvariational (so-called Hill-determinant) intuitive identification of binding energies with zeros of certain infinite determinants may be given a rigorous mathematical foundation. The essence of the construction lies in an appropriate restriction of the class of the admissible Ansätze. This eliminates the undesirable confluence of the physical and unphysical components of ψ(r) that may take place in the general case.
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    A new proof of the generalized Birkhoff theorem (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1440-1441 
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    Notes: A new proof of the generalized Birkhoff theorem in general relativity is presented. The partial results contained in previous proofs are recovered in a unified treatment of the different kinds of space-times to which the theorem applies. The proof is based on the fact that these space-times are conformal to the direct product of two two-dimensional manifolds (almost-product structure).
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    The S¯(a,b,c/m) metrics interpreted as colliding wave solutions (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1442-1442 
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    Notes: It is shown that the class of solutions S¯(a,0,−1/1), a real slice of the "complexified'' Plebanski S(a,b,c/m) metrics, is interpretable as colliding wave solutions and, for a=−s2, coincides precisely with the Ferrari–Ibañez colliding wave metrics.
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    Hauser–Malhiot spaces admitting a perfect fluid energy-momentum tensor (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1445-1450 
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    Notes: In this paper a special case of Hauser–Malliot (HM) space-times is examined in the presence of a perfect fluid source. The obtained solutions are all known except for a generalization of a stationary axisymmetric solution found by Kramer [Class. Quantum Gravit. 1, L3 (1984)].
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    On self-similar Tolman models (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1443-1444 
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    Notes: The self-similar spherically symmetric solutions of the Einstein field equation for the case of dust are identified. These form a subclass of the Tolman models. These self-similar models contain the solution recently presented by Chi [J. Math. Phys. 28, 1539 (1987)], thereby refuting the claim of having found a new solution to the Einstein field equations.
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    Real anomalies (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1455-1464 
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    Notes: The relationship between global anomalies of quantum theory and the topology of spaces of real Fredholm operators is shown. The spectral properties of such operators and how they are seen in examples of global anomalies on both compact and noncompact space-times are discussed.
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    Conformally Ricci-flat perfect fluids. II (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1451-1454 
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    Notes: A review is given of the perfect fluid solutions which can be constructed by conformal transformations of nonflat vacuum solutions of Einstein's field equations. In addition a proof is given that (a) under physically reasonable restrictions all solutions for which the gradient of the scalar field is orthogonal to the fluid velocity and (b) all solutions sharing with the corresponding vacuum solution a symmetry group of dimension n≥2 are necessarily shear- or vorticity-free and hence are explicitly known.
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    Collapse and exponentiation of infinite symmetry algebras of Euclidean projective and Grassmannian σ models (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1465-1471 
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    Notes: Various two-dimensional σ models enjoy an infinite set of infinitesimal transformations acting on their solution space. The action of these symmetries is investigated for the Euclidean projective and Grassmannian σ models. On the (anti-) self-dual sector of the latter, the algebra of symmetries is shown to collapse to a finite-dimensional algebra isomorphic to sl(n+1,C) for the models with fields in the Grassmannians Gn+1,p. The finite action obtained by exponentiation is given in a closed form. For CPn models, this result is extended to the whole space of finite action solutions and the structure of the algebra remains sl(n+1,C). Hence the action is not transitive on the solution space.
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    The solution of the s-wave Bethe–Goldstone equation with a standard hard core potential (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1477-1485 
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    Notes: This paper extends the results of an earlier article [J. Math. Phys. 27, 1154 (1986)] to include the solution of the s-wave Bethe–Goldstone equation for the interaction of two nucleons characterized by a potential with an infinite repulsive core and a nearby attractive well. The solution again exhibits band-limiting behavior and is obtained in closed form via the prolate spheroidal wave functions. It is shown that the attractive part of the interaction potential perturbs the far-field scattered wave so that healing of the nucleon wave function is achieved only when the attractive part is weak. Finally, asymptotic results for the case of small core radius are also calculated.
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    On the quantization of Poincaré and de Sitter gauge models (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1472-1476 
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    Notes: The gauge model based on the Yang–Mills equations for the Poincaré group cannot be consistently quantized, at least in a perturbative approach. The regulated theory, obtained by adding the counterterms required by consistency and renormalizability, is just the gauge theory for a de Sitter group.
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    Variational nature of dispersion equations revisited (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1486-1497 
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    Notes: Corrections and clarifications are made of some past treatments of the variational nature of the eigenfrequency calculation for dispersion equations and new results are presented. The main conclusions are the following: (1) Any relation between a normal mode and its dual must be consistent with the fact that the boundary conditions satisfied by the normal mode may differ from the adjoint boundary conditions satisfied by the dual. This will affect whether or not a given bilinear form will yield a variational result for the eigenfrequency. (2) If a dispersion matrix is constructed from the dispersion operator by using left and right basis functions that satisfy homogeneous boundary conditions on the dual eigenfunction and the eigenfunction, respectively, then generally a second-order accurate eigenfrequency is obtained by solving the matrix form of the dispersion equation. (3) When solving for the normal modes in terms of perturbation potentials, the adjoint boundary conditions are gauge dependent. For cases where the adjoint boundary conditions allow only the trivial solution for the dual eigenfunction, it may be possible to obtain variational results for the eigenfrequency by requiring that the trial functions for the normal mode and its dual satisfy variational boundary conditions.
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    Spectral properties of an optical polaron in a magnetic field (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1498-1504 
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    Topics: Mathematics , Physics
    Notes: An optical polaron, which is exposed to a homogeneous magnetic field, is considered. Making use of functional analytical methods of Fröhlich [Fortschr. Phys. 22, 159 (1974)], it is proved that the ground-state energy, the magnetic polaron mass, and the number of virtual phonons in the ground state are analytical functions of the electron–phonon coupling parameter and the magnetic field strength. Consequently, a discontinuous stripping transition, which was claimed recently by several authors, does not exist. In fact, some authors have stated that the discontinuities they encounter might indeed be artifacts due to the approximation. The spectrum of the momentum-decomposed Fröhlich Hamiltonian is analyzed; bounds and smoothness properties of the ground state and the discrete excited states are derived. All results hold also for lower spatial dimensions.
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    Analytical behavior of the ground-state energy and pinning transitions for a bound polaron (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1505-1513 
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    Notes: Spectral properties of a three-dimensional optical polaron, bound in an external potential, are studied. If the associated one-particle Hamiltonian has a bound state, it is proved that the ground-state energy of the polaron and expectation values of the ground state are analytical functions of the coupling parameter α and the potential strength β. Especially in the case of a Coulomb potential, all changes in the polaron state are continuous, disproving claims of several variational calculations. If, on the other hand, the one-particle Hamiltonian has no bound state, the existence of a pinning transition is shown for the polaron. As physically relevant potentials for the pinning transition, a spherical square well and a screened Coulomb potential are considered. Their phase diagrams are given in the effective-mass approximation.
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    The Vaidya–Patel solution with Robertson–Walker metric as a rotating inflationary scenario (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1514-1517 
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    Notes: The Vaidya–Patel solution of a rotating homogeneous fluid in the presence of a Maxwellian source-free electromagnetic field is interpretated as an inflationary scenario with a gauge field with local U(1) symmetry, a vacuum energy, and a rotating perfect fluid. An explicit solution is found to be expressible in terms of known solutions representing the radiation filled Robertson–Walker universe with a cosmological term. In the case that the rotating fluid is radiation, the discussion of the model is considerably simplified. How the time scale of transition into a pseudo-de Sitter stage, as observed by an observer following the rotating fluid, is affected by vorticity is also studied.
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    Erratum: Canonical formalism of dissipative fields in the thermo field dynamics [J. Math. Phys. 28, 2741 (1987)] (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1518-1518 
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    A representation of SO(p+q,p+q) on SO(p,q) (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1079-1082 
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    Notes: A construction of a representation of SO(p+q,p+q) by operators on SO(p+q) is presented, connected with a relativistic top kinematics. In addition to a first-order differential operator part there is a multiplicative term containing a parameter λ in some of the generators. It is shown by the explicit evaluation of the corresponding Casimir invariants that the representation (λ,...,λ), λ=0, 1/2 ,1,..., is realized by this construction.
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    Complex structure on a real Hilbert space and symplectic structure on a complex Hilbert space (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1069-1078 
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    Notes: Alternative ways of complexifying a real Hilbert space and quaternionizing a complex Hilbert space are described. The work gives some insight into why even though in the finite-dimensional case a complex Hilbert space when viewed as a real Hilbert space and a quaternionic Hilbert space when viewed as a complex Hilbert space have twice their original dimensions, the degrees of freedom of the linear operators remain unchanged. Many ramifications are discussed, among them the reconciliation of the linearity of the adjoint of a semilinear (antilinear) map from one complex Hilbert space to another with the semilinearity (antilinearity) of the adjoint of a semilinear (antilinear) map from one complex Hilbert space to itself. Groundwork is prepared for the study of the noncommutative algebra of additive operators on a quaternionic Hilbert space.
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    Substitutional symmetries and extra degeneracies of real symmetric matrices (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1091-1096 
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    Notes: The relation between substitutional symmetry operations that leave a real symmetric matrix invariant and the degeneracies exhibited by the matrix in diagonal form are examined. The usual application of group theory to this problem is formulated. Substitutional (and other) symmetries can exist, which do not form part of the invariance group. These symmetries can cause extra degeneracy of the root system and are frequently encountered in some physical applications such as the Hückel model of molecular bonds. Some general features that lead to extra degeneracy are noted and illustrative examples are given for systems of six equivalent centers.
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    Locally operating realizations of nonconnected transformation Lie groups (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1083-1090 
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    Notes: A systematic study of locally operating multiplier realizations of nonconnected Lie groups of transformations is presented that generalizes previous results on connected groups. The semilinear locally operating multiplier realizations of a nonconnected group G are those obtained through an induction process from the finite-dimensional semilinear representations of a given subgroup of a representation group G¯ for G.
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    Evaluation of Feynman diagrams in the logarithmic approach to quantum field theory (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 2659-2665 
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    Notes: The techniques necessary to compute the O(δ2) contributions to the Green's functions of a scalar field theory with self-interaction λ(φ2)1+δ in d-dimensional space-time are developed. The resulting expressions are evaluated explicitly for d=1, 0, and some negative even dimensions. For d=3 and 4 we calculate their leading behavior in terms of a spatial cutoff a.
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    On the Painlevé property of nonlinear field equations in 2+1 dimensions: The Davey–Stewartson system (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 2666-2671 
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    Notes: With the purpose of clarifying some aspects of the complete integrability of nonlinear field equations, a singular-point analysis is performed of the Davey–Stewartson system, which can be considered as an extension in 2+1 dimensions of the nonlinear Schrödinger equation. It is found that the system under consideration possesses the Painlevé property and allows a set of Bäcklund transformations obtained by truncating the series expansions of the solutions about the singularity manifold.
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    Periodic reduction of self-dual Yang–Mills equations (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 2672-2674 
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    Notes: A class of GL(∞)-invariant self-dual Yang–Mills (SDYM) equations is considered. It is shown that the GL(∞) SDYM equations are reduced to the GL(n,C) SDYM hierarchy by imposing a periodic condition. This reduction procedure makes clear a relationship between our GL(∞) SDYM equations and the usual infinite matrix representation of a single GL(n,C) SDYM equation.
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    Electromagnetic scattering for a class of anisotropic layered media (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 2675-2681 
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    Notes: The problem of computing fields produced by currents in the presence of unflawed layered media is reduced to quadrature. Each layer either has single-axis-type anisotropy or is isotropic. Integral equations are derived for fields in the presence of layered media with flaws.
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    On biorthogonal and orthonormal Clebsch–Gordan coefficients of SU(3): Analytical and algebraic approaches (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 2351-2366 
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    Notes: Minimal biorthogonal systems of the Clebsch–Gordan (Wigner) coefficients of SU(3)&supuline;U(2) are discussed as well as the dual coupled bases. The closed system of analytical expressions for the dual isofactors (reduced Wigner coefficients) and the overlaps of coupled states is obtained with the help of analytical inversion symmetry. The Regge-type symmetry of the overlaps and the boundary orthonormal isofactors (orthogonalization coefficients) is discovered. The polynomial structure of the alternative complete algebraic systems of the orthonormal SU(3) isofactors (characterized by the null spaces, symmetries, and additional selection rules and obtained by means of the Hecht or Gram–Schmidt process) is considered. The realizations of the external "missing label'' operators of the third and the fourth orders in the minimal coupled bases, which lead to preferable algorithms to evaluate the orthonormal SU(3) coupling coefficients satisfying different symmetry properties, are presented. With the help of the 6j coefficients of SU(2) or inverted truncated SU(2) recoupling matrices, the biorthogonal systems associated with the SU(3) canonical tensor operators are expanded in terms of minimal ones.
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    Characteristic functions and higher order Lagrangians (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1122-1126 
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    Notes: In the context of the extension of the Hamilton–Jacobi theory to include Lagrangians involving higher derivatives the characteristic function seems not to have been considered. This omission is here rectified.
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  • 88
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    Finitely many δ interactions with supports on concentric spheres (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 660-664 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Using the theory of self-adjoint extensions of symmetric operators the precise mathematical definition of the quantum Hamiltonian describing a finite number of δ interactions with supports on concentric spheres is given. Its resolvent is also derived, its spectral properties are described, and it is shown how this Hamiltonian can be obtained as a norm resolvent limit of a family of local scaled short-range Hamiltonians.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528005
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    Complete orthonormal sets on the past light cone. I. Functions belonging to mass zero and helicity s (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 636-641 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This is the first of a series of papers preparing the mathematical framework for a past light-cone formulation for the quantum mechanics of particles of arbitrary mass and spin. The aim of past light-cone quantum theory is to define quantum states solely in terms of data accessible to an observer, i.e., information from within his current past light cone. In order to set up such a theory one needs to define on the past light cone complete orthonormal sets of functions that belong to the appropriate unitary irreducible representation of the Poincaré group. Such functions are interpreted as energy-momentum eigenfunctions. The present paper treats the discrete spin, zero mass case for all values of the helicity s=0, 1/2 , (3)/(2) ,. . . .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528003
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    The structure of the Clifford algebra (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 2338-2345 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The properties of the Clifford algebra are concisely summarized in four identities that extend the usual Lie algebra to the entire algebra. This formulation may be used to analyze the general structure of the Clifford algebra, but it is found that the symmetry properties are not consistent with the geometrical content. The extension of the graded Lie algebra to the entire algebra generates a geometrical algebra which simplifies the analysis of the structure of the Clifford algebra. This produces a direct proof of the fundamental theorem that relates the Clifford and Grassmann algebras via the Pfaffian.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528117
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    Clifford associativity and the Pfaffian expansion (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 2346-2350 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: With the help of the Pfaffian, an operator on the tensor algebra which generates the explicit coset structure of the Clifford quotient of the tensor algebra is defined. The associativity property of this tensor representation of Clifford algebra leads to a Pfaffian expansion analogous to the Laplace expansion of a determinant. Further, the explicit statement of the algebra norm provides a proof for the Hadamard theorem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528118
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    The Pauli matrices in n dimensions and finest gradings of simple Lie algebras of type An−1 (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 665-673 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Properties of the Lie algebra gl(n,C) are described for a basis which is a generalization of the 2×2 Pauli matrices. The 3×3 case is described in detail. The remarkable properties of that basis are the grading of the Lie algebra it offers (each grading subspace is one dimensional) and the matrix group it generates [it is a finite group with the center of SL(n,C) as its commutator group].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528006
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    Some new stationary axisymmetric asymptotically flat space-times obtained from Painlevé transcendents (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 674-680 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For the stationary axisymmetric Einstein vacuum equations in cylindrical coordinates we find that both the Ernst equation and the two real equations which alternatively describe the stationary axisymmetric problem separate, leading to Painlevé transcendents. The boundary and asymptotic behaviors of the resulting space-times are investigated in both cases. Two families of solutions are determined which, away from the symmetry axis, become asymptotically flat. The analysis provides an example to the conjecture that the Painlevé property implies integrability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528201
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    Colliding gravitational plane waves with noncollinear polarization. III (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 681-689 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Hauser–Ernst homogeneous Hilbert problem (HHP) approach, formerly used in connection with the derivation of stationary axisymmetric fields, is here adapted to the derivation of colliding gravitational plane wave solutions of the vacuum Einstein equations. Proceeding from Kasner metrics, and using a double-Harrison transformation, the HHP approach yields a three-parameter generalization of a two-parameter family of colliding wave solutions found recently by Ferrari, Ibañez, and Bruni. In the present paper we provide the details concerning the derivation of this new family of solutions, and we set the stage for future applications of the HHP approach in connection with gravitational waves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528007
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    On the collision of planar impulsive gravitational waves (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 690-695 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Exact continuous solutions to the Einstein field equations are determined under the assumption that the subspaces of space-time spanned by the variables XA (A=1,2) admit the three-dimensional group of motions of a two-plane, and the Ricci tensor RAB (A,B=1,2) vanishes. The space-time is assumed to contain two colliding planar impulsive gravitational waves. Each wave may be followed by a distribution of null dust. It is shown that the Cauchy data on a spacelike three-surface does not lead to a unique solution of the Einstein field equations unless additional requirements are imposed on the stress-energy tensor in the region of interaction of the waves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528008
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    Multiplication formulas of orthogonal polynomials of boson field operators: Derivation based on the generalized phase-space method (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 696-701 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The products of several orthogonal polynomials of boson field operators, the quantum mechanical version of multiple Wiener integrals, are expressed as linear combinations of the polynomials. The expression is obtained by making use of the correspondence rules of boson operators and complex numbers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528009
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    The covariant effective action in QED. One-loop magnetic moment (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 702-708 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The paper starts the program of rewriting quantum electrodynamics in terms of the manifestly covariant and covariantly computed effective action. A general method for obtaining nonlocal terms in the effective action is proposed and the term responsible for the one-loop magnetic moment of the electron is worked out. In contrast to the usual calculation based on Green's functions, the present calculation nowhere encounters the infrared divergences (including renormalization and restriction to the physical mass shell). Comparison with the method of Green's functions shows the inadequacy of the latter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528010
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    Moment problem formulation of the simplified ideal magnetohydrodynamics ballooning equation (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 717-720 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A fundamentally new method for determining the eigenvalues of linear differential operators is presented. The method involves the application of moment analysis and affords a fast and precise numerical algorithm for eigenvalue computation, particularly in the intermediate and strong coupling regimes. The most remarkable feature of this approach is that it provides exponentially converging lower and upper bounds to the eigenvalues. The effectiveness of this method is demonstrated by applying it to an important magnetohydrodynamics problem recently studied by Paris, Auby, and Dagazian [J. Math. Phys. 27, 2188 (1986)]. Through the very precise lower and upper bounds obtained, this approach gives full support to their analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528012
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    Spin-polarized Thomas–Fermi theory (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 709-716 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Of concern is a rigorous Thomas–Fermi theory of electron densities for spin-polarized quantum-mechanical systems. The number N↑, N↓ of spin-up and spin-down electrons are specified in advance, and one seeks to minimize the energy functional E(ρ↑,ρ↓) =c1∫R3(ρ↑(x)5/3 +ρ↓(x)5/3)dx +c2∫R3∫R3[ρ(x)ρ(y)/||x −y||]dx dy +∫R3V(x)ρ(x)dx, where c1, c2 are given positive constants, ρ↑ and ρ↓ are non-negative functions, ρ=ρ↑ +ρ↓ is the total electron density, ∫R3ρ↑(x)dx =N↑, ∫R3ρ↓(x)dx =N↓, and V is a given potential. These results are analogous to the classical rigorous (spin-unpolarized) Thomas–Fermi theory developed by Lieb and Simon [Phys. Rev. Lett. 33, 681 (1973)] and by Bénilan and Brezis ("The Thomas–Fermi problem,'' in preparation).
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    URL: http://dx.doi.org/10.1063/1.528011
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    Erratum: The diffraction of waves by a penetrable ribbon [J. Math. Phys. 4, 65 (1963)] (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 721-722 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528013
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