Feynman's operational calculi: Disentangling away from the origin
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.
scientific article; zbMATH DE number 5712238