Path Integral Quantization Hb

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 mechanics and quantum mechanics in the Dirac operator and state formalism, and further examination of the path integral. The second part examines relativistic field theories, reviewing special relativity, as well as derivation of the path integral representation of the vacuum transition element for quantized scalar, spinor, and vector fields from the coherent state representation of the respective field theories. * Concise introduction to the derivation and methods of path integral approaches to quantum mechanics and quantum field theory. * Self-contained guide for students and practitioners PRELIMS.pdf Preface Outline placeholder Further reading Author biography Mark S Swanson CH001.pdf Chapter 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 Further reading CH002.pdf Chapter 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 Further reading CH003.pdf Chapter 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 Further reading CH004.pdf Chapter 4 Quantum field theory and path integrals 4.1 Special relativity and relativistic notation 4.2 Action functionals and relativistic fields 4.2.1 The free scalar field 4.2.2 The free bispinor field 4.2.3 The free vector or gauge field 4.3 Canonical quantization of free fields 4.3.1 Quantizing the free scalar field 4.3.2 Quantizing the free bispinor field 4.3.3 Quantizing the free gauge field 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 Further reading CH005.pdf Chapter 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 Further reading 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 mechanics and quantum mechanics in the Dirac operator and state formalism, and further examination of the path integral. The second part examines relativistic field theories, reviewing special relativity, as well as derivation of the path integral representation of the vacuum transition element for quantized scalar, spinor, and vector fields from the coherent state representation of the respective field theories. Key Features Concise introduction to the derivation and methods of path integral approaches to quantum mechanics and quantum field theory.Self-contained guide for students and practitioners "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 mechanics and quantum mechanics in the Dirac operator and state formalism, and further examination of the path integral. The second part examines relativistic field theories, reviewing special relativity, as well as derivation of the path integral representation of the vacuum transition element for quantized scalar, spinor, and vector fields from the coherent state representation of the respective field theories." -- Prové de l'editor