2010•New York journal of mathematicsRequires access

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

Lance Nielsen

Abstract

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.

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Key concepts: Cauchy's integral formula, Mathematics, Cauchy distribution, Methods of contour integration, Kernel (algebra), Cauchy principal value, Cauchy's integral theorem, Function (biology)