Milton K.A. Schwinger's Quantum Action Principle: From Dirac’s Formulation Through Feynman’s Path Integrals, the Schwinger-Keldysh Method, Quantum Field Theory, to Source Theory

Springer, 2015. - 116 pp.
Starting from the earlier notions of stationary action principles, these tutorial notes shows how Schwinger’s Quantum Action Principle descended from Dirac’s formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. Part I brings out in more detail the connection between the two formulations, and applications are discussed. Then, the Keldysh-Schwinger time-cycle method of extracting matrix elements is described. Part II will discuss the variational formulation of quantum electrodynamics and the development of source theory.Historical Introduction.
Review of Classical Action Principles.
Classical Field Theory—Electrodynamics.
Quantum Action Principle.
Time-Cycle or Schwinger-Keldysh Formulation.
Relativistic Theory of Fields.
Nonrelativistic Source Theory.
Concluding Remarks.