Lays the foundations of the theory of fluctuating multivalued fields. This title includes phenomena dominated by the statistical mechanics of line-like objects, such as the phase transitions in superfluids and superconductors as well as the melting process of crystals, and the electromagnetic potential as a multivalued field.

Provides students and researchers with supplementary reading material for graduate courses on phase transitions, quantum field theory, gravitational physics, and differential geometry. This book lays the foundations of the theory of fluctuating multivalued fields with numerous applications.

This work explains in detail how to perform perturbation expansions in quantum field theory to high orders, and how to extract the critical properties of the theory from the resulting divergent power series. These properties are calculated for various second-order phase transitions of three-dimensional systems with high accuracy, in particular the critical exponents observable in experiments close to the phase transition. Beginning with an introduction to critical phenomena, this book develops the functional-integral description of quantum field theories, their perturbation expansions, and a...

This is the fourth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. The second is a simple quantum equivalence principle...