Malliavin calculus and Euclidean quantum mechanics. I: Functional calculus
type: Item
instance of: scholarly article
title: Malliavin calculus and Euclidean quantum mechanics. I: Functional calculus
zbMATH Open document ID: 0733.35093
DOI: 10.1016/0022-1236(91)90073-E
author: Ana Bela Cruzeiro
author: Jean-Claude Zambrini
published in: Journal of Functional Analysis
publication date: 1991-01-01T00:00:00Z
review text: The authors state that they give a rigorous version of the functional calculus developed by R. Feynman in relation to his path integral formulation of quantum mechanics, their approach is Euclidean but distinct from the one founded on the Feynman-Kac formula. It uses two basic ingredients, a new probabilistic interpretation of the classical heat equation, introduced recently in the frame work of Euclidean Quantum Mechanics, and an infinite dimensional differential calculus adapted to functionals of the diffusion processes relevant for this interpretation.
reviewed by: Y.Suyama
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 81Q30
zbMATH DE Number: 4212642
zbMATH Keywords: Malliavin calculus
zbMATH Keywords: functional calculus
zbMATH Keywords: Feynman-Kac formula
MaRDI profile type: Publication
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full work available at URL: 0022-1236(91)90073-e
OpenAlex ID: W1990794131
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description: scientific article; zbMATH DE number 4212642