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Title: The semiclassical coherent state propagator in the Weyl representation

It is shown that the semiclassical coherent state propagator takes its simplest form when the quantum mechanical Hamiltonian is replaced by its Weyl symbol in defining the classical action, in that there is then no need for a Solari-Kochetov correction. It is also shown that such a correction exists if a symbol other than the Weyl symbol is chosen and that its form is different depending on the symbol chosen. The various forms of the propagator based on different symbols are shown to be equivalent provided the correspondingly correct Solari-Kochetov correction is included. All these results are shown for both particle and spin coherent state propagators. The global anomaly in the fluctuation determinant is further elucidated by a study of the connection between the discrete fluctuation determinant and the discrete Jacobi equation.
Authors:
; ;  [1] ;  [2]
  1. Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208 (United States)
  2. Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green St., Urbana, Illinois 61801 (United States)
Publication Date:
OSTI Identifier:
22479565
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 12; Other Information: (c) 2015 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; ANNIHILATION OPERATORS; CORRECTIONS; EIGENSTATES; EQUATIONS; FLUCTUATIONS; HAMILTONIANS; PROPAGATOR; QUANTUM MECHANICS; SEMICLASSICAL APPROXIMATION; SPIN