Wiener Integration for Quantum Systems: A Unified Approach to the Feynman-Kac formula

Details Wiener Integration for Quantum Systems: A Unified Approach to the Feynman-Kac formula Wiener Integration for Quantum Systems: A Unified Approach to the Feynman-Kac formula

1997-03-18

arxiv.org/abs/quant-ph/9703031v1

Path integrals: Dubna '96, eds. V. S. Yarunin and M. A. Smondyrev, Dubna 1996, JINR E96-321, ISBN: 5-85165-451-1, pp. 95-106 (

Physics

Quantum Physics

12 pages, LATEX

Scientific paper

A generalized Feynman-Kac formula based on the Wiener measure is presented. Within the setting of a quantum particle in an electromagnetic field it yields the standard Feynman-Kac formula for the corresponding Schr\"odinger semigroup. In this case rigorous criteria for its validity are compiled. Finally, phase-space path-integral representations for more general quantum Hamiltonians are derived. These representations rely on a generalized Lie-Trotter formula which takes care of the operator-ordering multiplicity, but in general is not related to a path measure.

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