Non-Perturbative Quantum Field Theory : Mathematical Aspects and Applications

Mathematical Aspects and Applications

By: Jurg Frohlich (Editor)

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Hardcover | 1 December 1989

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854 Pages

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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.

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"These papers contain much that was original, but, perhaps more significantly for a collection, they provide a remarkable overview of a large body of work." Mathematical Reviews

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Foreword
Introduction	p. 1
Phase Transitions and Continuous Symmetry Breaking
"Phase transitions, Goldstone bosons and topological superselection rules"	p. 27
"The pure phases (harmonic functions) of generalized processes" or "Mathematical physics of phase transitions and symmetry breaking"	p. 164
"Spontaneously broken and dynamically enhanced global and local symmetries"	p. 193
Non-Perturbative Quantization of Topological Solitons
"Quantum theory of non-linear invariant wave (field) equations" or "Super selection sectors in constructive quantum field theory"	p. 215
"Bosonization, topological solitons and fractional charges in two-dimensional quantum field theory"	p. 290
"Quantum skyrmions"	p. 337
"Variational problems on vector bundles"	p. 359
Gauge Theories, including (the Infrared Problem in) Quantum Electrodynamics
"Charged sectors and scattering states in quantum electrodynamics"	p. 395
"Magnetic monopoles and charged states in four-dimensional, abelian lattice gauge theories"	p. 439
"Some results and comments on quantized gauge fields"	p. 447
"Some comments on the crossover between strong and weak coupling in SU(2) pure Yang-Mills theory"	p. 477
"Quantum field theory of anyons"	p. 490
Triviality of [actual symbols not reproducible]
"On the triviality of [actual symbols not reproducible] theories and the approach to the critical point in [actual symbols not reproducible] 4 dimensions	p. 505
Random Geometry (Quantum Gravity and Strings)
"Regge calculus and discretized gravitational functional integrals"	p. 523
"The statistical mechanics of surfaces"	p. 546
Low-Dimensional QFT: Two-Dimensional Conformal Field Theory, Three-Dimensional (Gauge) Theories
"Statistics of fields, the Yang-Baxter equation, and the theory of knots and links"	p. 575
"Statistics and monodromy in two- and three-dimensional quantum field theory"	p. 605
"On the structure of (unitary) rational conformal field theory"	p. 620
"New developments in quantum field theory"	p. 629
"Two-dimensional conformal field theory and three-dimensional topology"	p. 660
"Quantum statistics and locality"	p. 739
"Universality in quantum Hall systems"	p. 793
Table of Contents provided by Blackwell. All Rights Reserved.

Non-Perturbative Quantum Field Theory : Mathematical Aspects and Applications

Mathematical Aspects and Applications

At a Glance

Hardcover

Industry Reviews

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