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Feynman maps, Cameron-Martin formulae and anharmonic oscillators. (English) Zbl 0578.28013

Summary: A Cameron-Martin formula is established for the Feynman map definition of the Feynman integral in non-relativistic quantum mechanics. This formula involves the Morse or Maslov indices and shows the connection with the Feynman-Hibbs definition of the path integral and the Fresnel integrals of Albeverio and Høegh-Krohn. Applications are given to the Feynman-Kac- Itô formula for anharmonic oscillator potentials.

MSC:

28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
81S40 Path integrals in quantum mechanics
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References:

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