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Schwinger's Quantum Action Principle

From Dirac’s Formulation Through Feynman’s Path Integrals, the Schwinger-Keldysh Method, Quantum Field Theory, to Source Theory

  • Book
  • © 2015

Overview

Authors:
  1. Kimball A. Milton

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

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Part of the book series: SpringerBriefs in Physics (SpringerBriefs in Physics)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter 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
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Keywords

About this book

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.

Reviews

“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)

Authors and Affiliations

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

    Kimball A. Milton

About the author

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.

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