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 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.

"Version: 20200801"

Conté: 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 re…