Feynman's Operational Calculus and Evolution Equations

摘要

We give an exposition and an extension of the ideas of Feynman's time-orderedoperational calculus for noncommuting operators. Various directions for 'disentangling' functions of such operators are provided by measures on the time intervals in question. We concentrate especially on exponentials of sums of noncommuting operators and prove that the unique solution of a broad class of evolution equations is given by the time-dependent operators arrived at by disentangling such exponential expressions.