Fermionic path integration and Grassmann Brownian motion
type: Item
instance of: scholarly article
title: Fermionic path integration and Grassmann Brownian motion
zbMATH Open document ID: 0642.60035
DOI: 10.1007/BF01221250
author: Alice Rogers
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: A Grassmann probability theory, with anticommuting random variables and stochastic processes, is developed using an extension of Berezin integration to infinite dimensional spaces. A Kolmogorov-type consistency condition allows integration on spaces of paths in anticommuting space. One particular stochastic process, Grassmann Brownian motion, is described and the associated measure used to give a path-integral formula for the kernel of the evolution operator in fermionic quantum mechanics. The Fourier mode expansion of Grassmann Brownian motion is derived.
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 81P20
zbMATH DE Number: 4046799
zbMATH Keywords: Kolmogorov-type consistency condition
zbMATH Keywords: integration on spaces of paths
zbMATH Keywords: Grassmann Brownian motion
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4046799