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Feynman integrals and Fredholm determinants. (English) Zbl 0816.46080

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 \((\hslash\to 0)\).

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
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[1] DOI: 10.1007/BF01389861 · Zbl 0449.35092 · doi:10.1007/BF01389861
[2] DOI: 10.1007/BF01947071 · Zbl 0493.35039 · doi:10.1007/BF01947071
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[5] DOI: 10.1063/1.530003 · Zbl 0785.40005 · doi:10.1063/1.530003
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