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Feynman Integral and Random Dynamics in Quantum Physics

A Probabilistic Approach to Quantum Dynamics

  • Zbigniew Haba

Part of the Mathematics and Its Applications book series (MAIA, volume 480)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Zbigniew Haba
    Pages 1-11
  3. Zbigniew Haba
    Pages 13-30
  4. Zbigniew Haba
    Pages 31-40
  5. Zbigniew Haba
    Pages 45-78
  6. Zbigniew Haba
    Pages 117-140
  7. Zbigniew Haba
    Pages 141-158
  8. Zbigniew Haba
    Pages 159-167
  9. Zbigniew Haba
    Pages 169-184
  10. Zbigniew Haba
    Pages 291-301
  11. Zbigniew Haba
    Pages 303-311
  12. Zbigniew Haba
    Pages 313-329
  13. Back Matter
    Pages 353-367

About this book

Introduction

The Feynman integral is considered as an intuitive representation of quantum mechanics showing the complex quantum phenomena in a language comprehensible at a classical level. It suggests that the quantum transition amplitude arises from classical mechanics by an average over various interfering paths. The classical picture suggested by the Feynman integral may be illusory. By most physicists the path integral is usually treated as a convenient formal mathematical tool for a quick derivation of useful approximations in quantum mechanics. Results obtained in the formalism of Feynman integrals receive a mathematical justification by means of other (usually much harder) methods. In such a case the rigour is achieved at the cost of losing the intuitive classical insight. The aim of this book is to formulate a mathematical theory of the Feynman integral literally in the way it was expressed by Feynman, at the cost of complexifying the configuration space. In such a case the Feynman integral can be expressed by a probability measure. The equations of quantum mechanics can be formulated as equations of random classical mechanics on a complex configuration space. The opportunity of computer simulations shows an immediate advantage of such a formulation. A mathematical formulation of the Feynman integral should not be considered solely as an academic question of mathematical rigour in theoretical physics.

Keywords

Markov chain Rang Theoretical physics computational physics mathematical physics quantum field theory quantum mechanics quantum physics random dynamical system stochastic differential equation stochastic processes

Authors and affiliations

  • Zbigniew Haba
    • 1
  1. 1.Institute of Theoretical PhysicsUniversity of WrocławWrocławPoland

Bibliographic information

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