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  • 1
    Electronic Resource
    Electronic Resource
    Companion equations for branes (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 4284-4292 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The quantum mechanical transition between a free particle Lagrangian and the Klein–Gordon field description of a free particle (particle-wave duality) is conjectured to extend to an analogous construction of relativistically invariant wave equations associated with strings and branes. Electromagnetic interactions in the two systems are discussed. It is emphasized that all integrable free field theories, including those of Dirac–Born–Infeld type, are associated with Lagrangians equivalent to divergences on the space of solutions of the equations of motion. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533342
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  • 2
    Electronic Resource
    Electronic Resource
    Moyal–Nahm equations (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2539-2548 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Various aspects of the Nahm equations in three and seven dimensions are investigated. The residues of the variables at simple poles in the seven-dimensional case form an algebra. A large class of matrix representations of this algebra is constructed. The large N limit of these equations is taken by replacing the commutators by Moyal brackets, and a set of nontrivial solutions in a generalized form of Wigner distribution functions is obtained. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532713
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  • 3
    Electronic Resource
    Electronic Resource
    Two-point quasifractional approximant in physics. Truncation error (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1470-1477 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The quasifractional approximation method is developed in a systematic manner. This method uses simultaneously the power series, and at a second point, the asymptotic expansion. The usual form of the approximants is two or more rational fractions, in terms of a suitable variable, combined with auxiliary nonfractional functions. Coincidence in the singularities in the region of interest is pursued. Equal denominators in the rational fractions is required so that the solution of only linear algebraic equations is needed to determine the parameters of the approximant. An upper bound is obtained for the truncation error for a certain class of functions, which contains most of the functions for which this method has been applied so far. It is shown that quasifractional approximants can be derived as a mixed German and Latin polynomial problem in the context of Hermite–Padé approximation theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529304
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  • 4
    Electronic Resource
    Electronic Resource
    Four-dimensional boson field theory. III. Nontriviality (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 1146-1158 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The results of numerical investigations based on series analysis indicate clearly that the method of phantom fields constructs nontrivial, self-interacting scalar Euclidean boson field theories. It is found that these continuum theories arise as the scaling limit to normal critical points of lattice statistical mechanical models. The character of these theories is numerically indistinguishable from that of a classical theory on the lambda line near the tricritical point.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527818
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  • 5
    Electronic Resource
    Electronic Resource
    Four-dimensional boson field theory. II. Existence (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 2379-2393 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The existence of the continuum, quantum field theory found by Baker and Johnson [G. A. Baker, Jr. and J. D. Johnson, J. Phys. A 18, L261 (1985)] to be nontrivial is proved rigorously. It is proved to satisfy all usual requirements of such a field theory, except rotational invariance. Currently known information is consistent with rotational invariance however. Most of the usual properties of other known Euclidean boson quantum field theories hold here, in a somewhat weakened form. Summability of the sufficiently strongly ultraviolet cutoff bare coupling constant perturbation series is proved as well as a nonzero radius of convergence for high-temperature expansions of the corresponding continuous-spin Ising model. The description of the theory by these two series methods is shown to be equivalent. The field theory is probably not asymptotically free.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527009
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  • 6
    Electronic Resource
    Electronic Resource
    Solving differential equations by a maximum entropy–minimum norm method with applications to Fokker–Planck equations (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1459-1463 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The method of maximum entropy–minimum norm is utilized to produce a general method of solving differential equations. The technique is a generalization and extension of previous work performed by Baker-Jarvis [J. Math. Phys. 30, 302 (1989)]. It is found that introducing an additional constraint on the norm of the solution vector produces a probability distribution that is integrable over the entire real axis. A number of simplifications occur. In this extended method the Lagrange multipliers and solution vector can be solved for explicitly, thus eliminating the necessity of solving systems of nonlinear equations for the Lagrange multipliers, as was required in the previous approach. It is shown that the solution obtained is equivalent to a minimum norm approximation. The maximum entropy solution of differential equations with Fourier moments is shown to be identical to a Fourier series solution. Additionally, the new method is applied to solving the random walk and Fokker–Planck equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528276
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  • 7
    Electronic Resource
    Electronic Resource
    Tensor product decompositions and branching rules of the N=2 superconformal algebra (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 1076-1094 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Tensor product decompositions of the N=2 superconformal algebras are examined to determine when they are finite or multiplicity-free, using various combinatorial identities. Using similar techniques, branching rules for the winding subalgebras of the N=2 superconformal algebras are investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530239
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  • 8
    Electronic Resource
    Electronic Resource
    Solution to boundary value problems using the method of maximum entropy (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 302-306 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The method of maximum entropy is used to solve a class of linear boundary value problems. The method is based on using various moments of the differential equation as constraints when maximizing the entropy. Various examples are presented and compared to exact solutions for varying numbers of moments. It is found that the maximum entropy approximation is, in many cases, better than a Fourier series solution for a given number of expansion terms and moments. The method is very general and will find applications in many areas of physics. A comparison of the amount of work necessary for the maximum entropy solution versus finite difference techniques is presented and it is found that the maximum entropy technique shows promise as an alternative solution technique.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528445
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