Chapter 10. Calculus of Variations: Applications

  1. Dr. Michio Masujima

Published Online: 27 NOV 2009

DOI: 10.1002/9783527627745.ch10

Applied Mathematical Methods in Theoretical Physics, Second Edition

Applied Mathematical Methods in Theoretical Physics, Second Edition

How to Cite

Masujima, M. (2009) Calculus of Variations: Applications, in Applied Mathematical Methods in Theoretical Physics, Second Edition, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527627745.ch10

Author Information

  1. Tokyo, Japan

Publication History

  1. Published Online: 27 NOV 2009
  2. Published Print: 19 AUG 2009

ISBN Information

Print ISBN: 9783527409365

Online ISBN: 9783527627745

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Keywords:

  • theoretical physics;
  • applied mathematical methods;
  • calculus of variations;
  • Hamilton–Jacobi Equation;
  • Quantum Mechanics;
  • action principle;
  • Schwinger–Dyson equation;
  • variational principle;
  • Poincare transformation;
  • Noether's theorem;
  • gauge principle;
  • path integral quantization;
  • BRST invariance;
  • lattice gauge field theory;
  • quark confinement;
  • WKB approximation;
  • Hartree–Fock equation

Summary

This chapter contains sections titled:

  • Hamilton–Jacobi Equation and Quantum Mechanics

  • Feynman's Action Principle in Quantum Theory

  • Schwinger's Action Principle in Quantum Theory

  • Schwinger–Dyson Equation in Quantum Field Theory

  • Schwinger–Dyson Equation in Quantum Statistical Mechanics

  • Feynman's Variational Principle

  • Poincare Transformation and Spin

  • Conservation Laws and Noether's Theorem

  • Weyl's Gauge Principle

  • Path Integral Quantization of Gauge Field I

  • Path Integral Quantization of Gauge Field II

  • BRST Invariance and Renormalization

  • Asymptotic Disaster in QED 475

  • Asymptotic Freedom in QCD 479

  • Renormalization Group Equations

  • Standard Model

  • Lattice Gauge Field Theory and Quark Confinement

  • WKB Approximation in Path Integral Formalism

  • Hartree–Fock Equation

  • Problems for Chapter 10