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Path Integral Quantization and Stochastic Quantization

  • Book
  • © 2009
  • Latest edition

Overview

Authors:
  1. Michio Masujima

    1. M.H. Company Ltd., 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/

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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 243-282
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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. Forthe description ofthe classical theory, we have two methods, one based on the Lagrangian formalism and the other based on the Hamiltonian formal­ ism. The Hamiltonian formalism is derived from the Lagrangian·formalism. In the standard formalism ofquantum mechanics, we usually make use ofthe Hamiltonian formalism. This fact originates from the following circumstance which dates back to the birth of quantum mechanics. The first formalism ofquantum 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". Based on the optical analogy, we obtain the Schrodinger equation as a result ofthe inverse of the Eikonal approximation to the Hamilton-Jacobi equation, and thus we arrive at "wave mechanics". The second formalism ofquantum mechanics is Heisenberg's "matrix me­ chanics". In this approach, we arrive at the Heisenberg equation of motion from consideration of the consistency of the Ritz combination principle, the Bohr quantization condition and the Fourier analysis of a physical quantity. These two formalisms make up the Hamiltonian.formalism of quantum me­ chanics.

Authors and Affiliations

  • M.H. Company Ltd., Tokyo, Japan

    Michio Masujima

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