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

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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.

Original languageEnglish (US)
Pages (from-to)463-488
Number of pages26
JournalNew York Journal of Mathematics
Volume16
StatePublished - Dec 1 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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