Variational derivatives of transformation functions in quantum field theory

Abstract

A systematic explicit derivation is given for variational derivatives of transformation functions in field theory with respect to parameters variations, also known as the quantum dynamical principle (QDP), by introducing, in the process, two unitary time-dependent operators which in turn allow an otherwise non-trivial interchange of the orders of the parameters variations of transformation functions with specific time-dependent ones. Special emphasis is put on dependent fields, as appearing, particularly, in gauge theories, and on the Lagrangian formalism. The importance of the QDP and its practicality as a powerful tool in field theory are spelled out, which cannot be overemphasized, and a complete derivation of it is certainly lacking in the literature. The derivation applies to gauge theories as well.