Rezende, Jorge Feynman integrals and Fredholm determinants. (English) Zbl 0816.46080 J. Math. Phys. 35, No. 8, 4357-4371 (1994). Summary: Simple properties of Feynman integrals such as the translation invariance, Fubini theorem, and Cameron-Martin formula are used in order to derive a product formula for Fredholm determinants. This formula enables us to compute explicitly some of such determinants as well as the index of the related Fredholm operators. Some examples are done which have applications in the semiclassical approximation \((\hslash\to 0)\). Cited in 4 Documents MSC: 46N50 Applications of functional analysis in quantum physics 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory 81S40 Path integrals in quantum mechanics 81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry Keywords:Feynman integrals; translation invariance; Fubini theorem; Cameron-Martin formula; product formula for Fredholm determinants; semiclassical approximation PDFBibTeX XMLCite \textit{J. Rezende}, J. Math. Phys. 35, No. 8, 4357--4371 (1994; Zbl 0816.46080) Full Text: DOI References: [1] DOI: 10.1007/BF01389861 · Zbl 0449.35092 · doi:10.1007/BF01389861 [2] DOI: 10.1007/BF01947071 · Zbl 0493.35039 · doi:10.1007/BF01947071 [3] DOI: 10.1007/BF01218758 · Zbl 0581.28009 · doi:10.1007/BF01218758 [4] Elworthy D., Ann. Inst. Henri Poincaré 41 pp 115– (1984) [5] DOI: 10.1063/1.530003 · Zbl 0785.40005 · doi:10.1063/1.530003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.