Feynman's operational calculus for families of noncommuting operators: tensor products, ordered supports, and the disentangling of an exponential factor
type: Item
instance of: scholarly article
title: Feynman's operational calculus for families of noncommuting operators: tensor products, ordered supports, and the disentangling of an exponential factor
zbMATH Open document ID: 1030.47008
DOI: 10.1023/A:1012903732597
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: In the early 1950s, R. Feynman proposed operational calculus as a kind of generalized path integral. Feynman was especially concerned with exponentiating sums of noncommuting operators. The main result of the paper under review is a mathematically rigorous formulation and proof of Feyman's formula and some related formulas for systems of not necessarily commuting bounded linear operators acting on a Banach space. This paper is closely related to the recent paper by the same authors [Russ. J. Math. Phys. 8, 153-171 (2001; Zbl 1027.46002)] and the monograph ``The Feynman integral and Fenman's operational calculus'' by \textit{G. W. Johnson} and \textit{M. Lapidus} [Oxford Mathematical Monographs, Clarendon Press, Oxford (2000; Zbl 0952.46044)].
reviewed by: Michael Perelmuter
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 47A13
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 58D30
zbMATH DE Number: 1927813
zbMATH Keywords: Feynman operational calculus
zbMATH Keywords: systems of bounded linear operators
author: Brian Jefferies
author: G. W. Johnson
MaRDI profile type: Publication
full work available at URL: a:1012903732597
OpenAlex ID: W177499882
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description: scientific article; zbMATH DE number 1927813