Schwinger's Quantum Action Principle

1. Front Matter

   Pages i-viii

   PDF

2. Historical Introduction

   • Kimball A. Milton

   Pages 1-2

3. Review of Classical Action Principles

   • Kimball A. Milton

   Pages 3-14

4. Classical Field Theory—Electrodynamics

   • Kimball A. Milton

   Pages 15-29

5. Quantum Action Principle

   • Kimball A. Milton

   Pages 31-50

6. Time-Cycle or Schwinger-Keldysh Formulation

   • Kimball A. Milton

   Pages 51-61

7. Relativistic Theory of Fields

   • Kimball A. Milton

   Pages 63-90

8. Nonrelativistic Source Theory

   • Kimball A. Milton

   Pages 91-112

9. Concluding Remarks

   • Kimball A. Milton

   Pages 113-114

10. Back Matter

    Pages 115-116

    PDF

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.

• Julian Schwinger
• Principle of Least Action in Quantum Mechanics
• Quantum Action Principle
• Schwinger-Keldysh Formulation
• Source Theory
• Variational Formulation of Quantum Mechanics

“The main goal of this short book is to examine quantum action principles and, in particular, the Schwinger action principle. … For anyone who is interested in a good but brief introduction to the subject, this monograph should be considered.” (Paul F. Bracken, Mathematical Reviews, April, 2016)

• Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, Norman, USA

  Kimball A. Milton

Professor Kimball Milton is the George Lynn Cross Research Professor of Physics at the University of Oklahoma. Kim Milton, a student of Julian Schwinger, studies in particular vacuum energy phenomena (the Casimir effect) in contexts ranging from cosmological through hadronic to condensed matter systems. He is the author, together with J Mehra of "Climbing the Mountain: The Scientific Biography of Julian Schwinger" Oxford University Press, 2000.

Policies and ethics