dorsal/arxiv
View SchemaWiener Integration for Quantum Systems: A Unified Approach to the Feynman-Kac formula
| Authors | B. Bodmann, H. Leschke, S. Warzel |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9703031 |
| URL | https://arxiv.org/abs/quant-ph/9703031 |
| Journal | 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 (with minor improvements) |
Abstract
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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"abstract": "A generalized Feynman-Kac formula based on the Wiener measure is presented.\nWithin the setting of a quantum particle in an electromagnetic field it yields\nthe standard Feynman-Kac formula for the corresponding Schr\\\"odinger semigroup.\nIn this case rigorous criteria for its validity are compiled. Finally,\nphase-space path-integral representations for more general quantum Hamiltonians\nare derived. These representations rely on a generalized Lie-Trotter formula\nwhich takes care of the operator-ordering multiplicity, but in general is not\nrelated to a path measure.",
"arxiv_id": "quant-ph/9703031",
"authors": [
"B. Bodmann",
"H. Leschke",
"S. Warzel"
],
"categories": [
"quant-ph"
],
"journal_ref": "Path integrals: Dubna \u002796, eds. V. S. Yarunin and M. A. Smondyrev,\n Dubna 1996, JINR E96-321, ISBN: 5-85165-451-1, pp. 95-106 (with minor\n improvements)",
"title": "Wiener Integration for Quantum Systems: A Unified Approach to the Feynman-Kac formula",
"url": "https://arxiv.org/abs/quant-ph/9703031"
},
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