Non-perturbative Quantum Field Theory: Mathematical Aspects And Applications

Compiled to illustrate the recent history of quantum field theory and its trends, this collection of selected reprints by Frohlich aims to be a comprehensive guide of the more mathematical aspects of the subject. Results and methods of the past 15 years are reviewed. The analytical methods employed are non-perturbative and, for the larger part, mathematically rigorous. Most articles are review articles surveying certain important developments in quantum field theory and guiding the reader towards the original literature. The theory of phase transitions and spontaneous symmetry breaking is reviewed in the first section. The second section discusses the non-perturbative quantization of topological solitons. The third section is devoted to the study of gauge fields. A paper on the triviality of (labda phi) to the power of 4 - theory in four and more dimensions is found in the fourth section, while the fifth contains two articles on "random geometry". The sixth and final part addresses topics in low-dimensional quantum field theory, including braid statistics, two-dimensional conformal field theory and an application to condensed matter theory. The volume begins with a comprehensive introduction by Jurg Frohlich.