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arxiv: quant-ph/9703031 · v1 · submitted 1997-03-18 · 🪐 quant-ph

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

classification 🪐 quant-ph
keywords formulafeynman-kacquantumgeneralgeneralizedmeasurerepresentationswiener
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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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