Description
Book SynopsisThis book aims to provide a quick pedagogical introduction to path integrals. It contains original material that never before has appeared in a book, for example the path integrals for the Wigner functions and for Classical Mechanics. This application to Classical Mechanics connects different fields like Hamiltonian mechanics and differential geometry, so the book is suitable for students and researchers from various disciplines.
Table of ContentsQuantum Mechanics and Summing Up Amplitudes; Double Slit Experiment; Infinite Slits Experiments and Path-Correspondence; Dirac's 1932 Paper on Small Time Amplitudes; Time-Slicing: From Infinitesimal to Finite Time Intervals; Re-derivation of the Feynman Path Integrals via the Trotter Formula; Free-Particle Propagator; Continuous Paths but Nowhere Differentiable; Path Integrals for Quadratic Potentials; WKB in the Operatorial Language; WKB in the Path-Integral Language; Introduction to the Formalism of Wigner Functions; Marinov's Path Integral for Wigner Functions; Semiclassical Expansion of Marinov's Work; The Work of Koopman and von Neumann (KvN) on the Operatorial Version of Classical Mechanics; Path Integral for Classical Mechanics (CPI) from the KvN Formalism; Cartan Calculus via the CPI; Geometric Quantization via the CPI; Non-Superposition Principle in Classical Mechanics and Degrees of Freedom; Going Beyond Classical Mechanics;
