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

摘要

In this paper we express the disentangling, or the formation of afunction of several noncommuting operators using Cauchy's IntegralFormula in several complex variables. It is seen that the disentanglingof a given function f can be expressed as a contour integral aroundthe boundary of a polydisk where the standard Cauchy kernel is replacedby the disentangling of the Cauchy kernel expressed as anelement of the disentangling algebra. This approach to the operationalcalculus allows for us to develop a "differential calculus''with disentanglings.