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Path Integral Quantization and Stochastic Quantization

  • Book
  • © 2000

Overview

Editors:
  1. Michio Masujima

    1. M.H. Company, Ltd, Tokyo, Japan, Tokyo, Japan

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  • Excellent overview
  • Important topic in elementary particle physics
  • Available online in LINK
  • All figures and references linked
  • Table of contents, introductions to chapters free for all
  • http://link.springer.de/series/stmp/
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Tracts in Modern Physics (STMP, volume 165)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-XII
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  2. Path Integral Representation of Quantum Mechanics

    Pages 1-54

  3. Path Integral Representation of Quantum Field Theory

    Pages 55-102

  4. Path Integral Quantization of Gauge Field

    Pages 103-174

  5. Path Integral Representation of Quantum Statistical Mechanics

    Pages 175-207

  6. Stochastic Quantization

    Pages 209-241

  7. Back Matter

    Pages 246-282
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Keywords

About this book

In this book, we discuss the path integral quantization and the stochastic quantization of classical mechanics and classical field theory. For the description of the classical theory, we have two methods, one based on the Lagrangian formalism and the other based on the Hamiltonian formal ism. The Harniltonian formalisni is derived from the Lagrangian formalism. In the standard formalism of quantum mechanics, we usually make use of the Hamiltonian formalism. This fact originates from the following circumstance which dates back to the birth of quantum mechanics. The first formalism of quantum mechanics is Schrodinger's wave mechan ics. In this approach, we regard the Hamilton Jacobi equation of analytical mechanics as the Eikonal equation of "geometrical mechanics". Bsed on the optical analogy, we obtain the Schrodinger equation as a result of the inverse of the Eikonal approximation to the Hamilton Jacobi equation, and thus we arrive at "wave mechanics" . The second formalism of quantum mechanics is Heisenberg's "matrix me chanics". In this approach, we arrive at the Heisenberg equation of motion frorn consideration of the consistency of the Ritz combination principle, the Bohr quantization condition and the Fourier analysis of a physical quantity. These two forrnalisrns make up the Hamiltonian formalism of quantum me chanics.

Editors and Affiliations

  • M.H. Company, Ltd, Tokyo, Japan, Tokyo, Japan

    Michio Masujima

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