Generalized measure permutation formulas in Feynman’s operational calculi

Abstract

Measure permutation formulas in Feynman’s operational calculi for noncommuting operators give relationships between the two operators \(\mathcal{T}_{\mu 1,\mu 2} f\left( {\tilde A,\tilde B} \right)\) and \(\mathcal{T}_{\mu 2,\mu 1} f\left( {\tilde A,\tilde B} \right)\). We develop generalized and iterated measure permutation formulas in the Jefferies-Johnson theory of Feynman’s operational calculi. In particular, we apply our formulas to derive an identity for a function of the Pauli matrices.