Feynman formulae and phase space Feynman path integrals for tauquantization of some LévyKhintchine type Hamilton functions
Evolution semigroups generated by pseudodifferential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the LévyKhintchine formula. The considered semigroups are represented as limits of nfold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudodifferential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynmanmore »
 Authors:

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 Bauman Moscow State Technical University, 2nd Baumanskaya street, 5, Moscow 105005, Russia and University of Saarland, Postfach 151150, D66041 Saarbrücken (Germany)
 University of Kaiserslautern, 67653 Kaiserslautern (Germany)
 Lomonosov Moscow State University, Vorob’evy gory 1, Moscow 119992 (Russian Federation)
 Publication Date:
 OSTI Identifier:
 22479639
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 2; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; FEYNMAN PATH INTEGRAL; HAMILTONIANS; KERNELS; LAGRANGIAN FUNCTION; MASS; PHASE SPACE; POTENTIALS; PROBABILITY; QUANTIZATION