Feynman's operational calculi: Disentangling away from the origin
type: Item
instance of: scholarly article
title: Feynman's operational calculi: Disentangling away from the origin
zbMATH Open document ID: 1196.47015
author: Lance Nielsen
published in: Acta Applicandae Mathematicae
publication date: 2010-05-26T00:00:00Z
review text: In quantum mechanics, one is often led to form functions of observables, which are operators on an infinite-dimensional Hilbert space. When the function in question involves products of noncommuting operators, a~functional calculus becomes difficult to develop. \textit{R.\,P.\thinspace Feynman} [Phys.\ Rev., II.\ Ser.\ 84, 108--128 (1951; Zbl 0044.23304)] gave a formulation of operational calculus for noncommuting operators with no attempt to maintain mathematical rigor. \textit{B.\,Jefferies} and \textit{G.\,W.\thinspace Johnson} [Russ.\ J.\ Math.\ Phys.\ 8, No.\,2, 153--171 (2001; Zbl 1186.81082)] equipped Feynman's ideas with a mathematical foundation. In the present paper, the author generalizes the work of Jefferies and Johnson to develop a method of forming functions of noncommuting operators using functions that are not necessarily analytic at the origin.
reviewed by: Miyeon Kwon
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 44A40
Mathematics Subject Classification ID: 47A13
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 81S99
zbMATH DE Number: 5712238
zbMATH Keywords: Feynman's operational calculus
zbMATH Keywords: disentangling
MaRDI profile type: Publication
full work available at URL: s10440-008-9428-7
OpenAlex ID: W1991736884
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DOI: 10.1007/S10440-008-9428-7
description: scientific article; zbMATH DE number 5712238