Path integral quantization /

This book is a self-contained and concise introduction to the techniques and applications of path integral quantization and functional techniques, aimed at students and practitioners. The first half of the text focuses on quantum mechanics, including a review of the action formulation of classical m...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Swanson, Mark S., 1947- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2020]
Colección:IOP ebooks. 2020 collection.
Temas:
Path integrals.
Quantum theory.
Quantum field theory.
Quantum physics (quantum mechanics & quantum field theory).
SCIENCE / Physics / Quantum Theory.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. Preliminaries
  • 1.1. Functionals and classical mechanics
  • 1.2. The operator formulation of quantum mechanics
  • 1.3. Operator identities
  • 1.4. Grassmann variables
  • 1.5. Gaussian integrals
  • 1.6. Poisson resummation
  • 2. The quantum mechanical path integral
  • 2.1. The infinitesimal transition element
  • 2.2. The basic quantum mechanical path integral
  • 2.3. The path in path integrals
  • 2.4. Discrete systems and path integrals
  • 2.5. Path integrals with singular coordinates and potentials
  • 2.6. The harmonic oscillator and coherent state path integrals
  • 2.7. Grassmann quantum mechanics and path integrals
  • 3. Evaluating the path integral
  • 3.1. Performing the intermediate integrations
  • 3.2. Classical paths and continuum methods
  • 3.3. The harmonic oscillator
  • 3.4. The semiclassical approximation
  • 3.5. Energy eigenfunctions and the path integral
  • 3.6. Coherent state path integrals and difference equations
  • 3.7. Generating functionals and perturbation theory
  • 3.8. The partition function
  • 3.9. Symmetry and canonical transformations
  • 3.10. Implementing constraints
  • 4. Quantum field theory and path integrals
  • 4.1. Special relativity and relativistic notation
  • 4.2. Action functionals and relativistic fields
  • 4.3. Canonical quantization of free fields
  • 4.4. Interacting fields and particle processes
  • 4.5. The interaction picture in field theory
  • 4.6. Coherent states and the scalar field path integral
  • 4.7. Coherent states and the Dirac bispinor path integral
  • 4.8. Configuration space techniques and quadratic path integrals
  • 4.9. The gauge field path integral
  • 5. Basic quantum field theory applications
  • 5.1. Perturbation theory
  • 5.2. Generating functionals
  • 5.3. Interaction symmetries and conservation laws
  • 5.4. Yang-Mills gauge field theory
  • 5.5. Non-perturbative aspects of 1 + 1 Yang-Mills theory
  • 5.6. The Dirac quantization condition
  • 5.7. The effective potential and spontaneously broken symmetry.

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