Non-Perturbative Quantum Field Theory

The following sections are included:

• FOREWORD

• CONTENTS

This book is a collection of some of my articles on non-perturbative aspects of quantum field theory. More than half of the papers reprinted here have a review character. Most of my review articles and many of my papers tend to be written under pressure of time and are therefore far from perfect. Thus, my ambition is, in general, limited to describing some ideas that I feel are beautiful or important, or both, and the main results that can be derived from them. It happens quite often that, in the course of the writing, I get sidetracked on a detour which, it later turns out, could have been avoided. Only rarely have I been able to do some rewriting or to pursue some scholarly ambitions going beyond the more obvious purposes of an article. The reader will notice that, for all these reasons - and, most certainly, for reasons rooted more deeply in my personality - most of the papers collected in this book have the character of sketches, even though they are sometimes rather elaborate and lengthy. I hope and believe that, in favourable cases, my sketches reproduce some of the main contours of what is being portrayed. However, the interested reader should take some time to rearrange the main lines of my drawing, or turn to the original sources, in order to understand more clearly what the main ideas and the main purpose of an article are…

The following reprint articles are included:

• PHASE TRANSITIONS, GOLDSTONE BOSONS AND TOPOLOGICAL SUPERSELECTION RULES

• THE PURE PHASES (HARMONIC FUNCTIONS) OF GENERALIZED PROCESSES OR: MATHEMATICAL PHYSICS OF PHASE TRANSITIONS AND SYMMETRY BREAKING

• SPONTANEOUSLY BROKEN AND DYNAMICALLY ENHANCED GLOBAL AND LOCAL SYMMETRIES

The following reprint articles are included:

• QUANTUM THEORY OF NON-LINEAR INVARIANT WAVE (FIELD) EQUATIONS OR: SUPER SELECTION SECTORS IN CONSTRUCTIVE QUANTUM FIELD THEORY

• Bosonization, Topological Solitons and Fractional Charges in Two-Dimensional Quantum Field Theory

• QUANTUM SKYRMIONS

• Variational Problems on Vector Bundles

The following reprint articles are included:

• Charged Sectors and Scattering States in Quantum Electrodynamics

• Magnetic Monopoles and Charged States in Four-Dimensional, Abelian Lattice Gauge Theories

• SOME RESULTS AND COMMENTS ON QUANTIZED GAUGE FIELDS

• Some Comments on the Crossover Between Strong and Weak Coupling in SU(2) Pure Yang–Mills Theory

• Quantum Field Theory of Anyons

The following reprint articles are included:

• ON THE TRIVIALITY OF THEORIES AND THE APPROACH TO THE CRITICAL POINT IN DIMENSIONS

The following reprint articles are included:

• REGGE CALCULUS AND DISCRETIZED GRAVITATIONAL FUNCTIONAL INTEGRALS

• THE STATISTICAL MECHANICS OF SURFACES

The following reprint articles are included:

• STATISTICS OF FIELDS, THE YANG-BAXTER EQUATION, AND THE THEORY OF KNOTS AND LINKS

• STATISTICS AND MONODROMY IN TWO- AND THREE-DIMENSIONAL QUANTUM-FIELD THEORY

• ON THE STRUCTURE OF (UNITARY) RATIONAL CONFORMAL FIELD THEORY

• New Developments in Quantum Field Theory

• TWO-DIMENSIONAL CONFORMAL FIELD THEORY AND THREE-DIMENSIONAL TOPOLOGY

• Quantum Statistics and Locality

• UNIVERSALITY IN QUANTUM HALL SYSTEMS