New York Journal of Mathematics
Volume 16 (2010) 463-488


Lance Nielsen

Feynman's operational calculi: using Cauchy's integral formula

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Published: November 20, 2010
Keywords: Feynman's operational calculus, disentangling, noncommuting operators
Subject: 32A05, 32A26, 47A10, 47A13

In this paper we express the disentangling, or the formation of a function of several noncommuting operators using Cauchy's Integral Formula in several complex variables. It is seen that the disentangling of a given function f can be expressed as a contour integral around the boundary of a polydisk where the standard Cauchy kernel is replaced by the disentangling of the Cauchy kernel expressed as an element of the disentangling algebra. This approach to the operational calculus allows for us to develop a "differential calculus'' with disentanglings.

Author information

Department of Mathematics, Creighton University, Omaha, NE 68178