Generalized infinite-dimensional Fresnel integrals.

DOI10.1016/j.crma.2003.11.022zbMath1038.58007OpenAlexW1975143760WikidataQ62049372 ScholiaQ62049372MaRDI QIDQ1426594

Sergio A. Albeverio, Sonia Mazzucchi

Publication date: 15 March 2004

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2003.11.022

zbMATH Keywords

oscillatory integralFeynman path integralanharmonic oscillator potentialGaussian integral

Mathematics Subject Classification ID

Applications of manifolds of mappings to the sciences (58D30)

Related Items (6)

The time-dependent quartic oscillator --- a Feynman path integral approach ⋮ An asymptotic functional-integral solution for the Schrödinger equation with polynomial potential ⋮ A global solution to the Schrödinger equation: From Henstock to Feynman ⋮ The mean value for infinite volume measures, infinite products, and heuristic infinite dimensional Lebesgue measures ⋮ Mathematical theory of Feynman path integrals ⋮ Feynman path integrals for the time dependent quartic oscillator

Cites Work

• Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics. I
• On the Schrödinger equation with potentials which are Laplace transforms of measures
• Feynman path integrals for polynomially growing potentials
• Finite dimensional approximation approach to oscillatory integrals and stationary phase in infinite dimensions
• Feynman integrals for a class of exponentially growing potentials
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