Schwinger's Quantum Action Principle: From Dirac's formulation through Feynman's path integrals, the Schwinger-Keldysh method, quantum field theory, to source theory

TL;DR

This paper traces the development of Schwinger's Quantum Action Principle from Dirac's initial ideas through Feynman's path integrals, the Keldysh-Schwinger method, and source theory, highlighting the continuity of concepts in quantum field theory.

Contribution

It provides a comprehensive historical and conceptual overview of the evolution of quantum action principles and their applications in quantum field theory and nonequilibrium physics.

Findings

Connection between Dirac's and Feynman's formulations clarified

Application of Keldysh-Schwinger method to nonequilibrium systems explained

Development of source theory and variational formulations discussed

Abstract

Starting from the earlier notions of stationary action principles, we show how Julian Schwinger's Quantum Action Principle descended from Dirac's formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. The connection between the two is brought out, and applications are discussed. The Keldysh-Schwinger time-cycle method of extracting matrix elements in nonequilibrium situations is described. The variational formulation of quantum field theory and the development of source theory constitute the latter part of this work. In this document, derived from Schwinger's lectures over four decades, the continuity of concepts, such as that of Green's functions, becomes apparent.