Path Integrals in Quantum Mechanics, Statistics and Polymer Physics

This textbook on the theory and applications of path integrals contains the solution to a number of non-trivial path integrals, most notably that of the Coulomb system. This has become possible by finding a consistent formulation of path integrals in spaces with curvature and torsion. Special emphasis is given to stability problems of path fluctuations in the presence of singular potentials such as centrifugal and angular barriers. The limitations of Feynman's time slicing procedure are exhibited and a new path integral formula is found which avoids the frequent danger of path collapse. The physically important applications to tunnelling problems are analyzed in detail. Their relevance to superconductivity and the large-order behaviour of perturbation expansions is demonstrated. The path integral description of equilibrium thermodynamics is presented, and an extension to non-equilibrium processes is presented. Much attention is paid to path integrals in spaces with topological restrictions. Their applications to entanglement problems in polymer physics and their relevance to particle statistics are discussed, also to the recently popular phenomenon of fractional statistics. Now in its second edition, the book has been extended by a more powerful variational approach which can now be applied to excited states and to tunnelling processes through high as well as low barriers. With it, the known large-order perturbation theory has been continued down to small orders. The book contains a detailed non-abelian Chern-Simons theory of polymer entanglement in terms of HOMFLY-polynomials and a discussion of anyonic aspects of the fractional quantum Hall effect and of high-Tc superconductivity. The semiclassical analysis incorporates now multidimensional systems to establish contact with recent work on chaos.