Renormalization and Invariance in Quantum Field Theory

The subject matter of this Advanced Study Institute, which has been rendered possible by the generous support of NATO, gratefully acknow ledged here, is of central importance to quantum field theory today. The problems involved are both deep and complicated, to a point that perhaps does not find easily a parallel in other branches of theoret ical physics. From the first rule-of-thumb prescriptions on how to perform renormalization to the most recent advances--which brighten our hopes to find, eventually, in field theory indications as to the ultimate composition of matter--a great amount of progress has cer tainly been made. We were fortunate to have among us many of the people who have most contributed to past and recent developments. Although clues that point to what to do next are clearer now than might have been expected only a few years ago, much hard work is still ahead. It is hoped that both our meeting, which brought to gether leaders in the field as well as bright and eager beginners, and the present volume, based on the NATO meeting, may be useful as a mise-a-point and as an up-to-date reference book for researchers interested in the field.

Contenu
Dimensional Renormalization.- A New Approach to Divergent Integrals.- Branching Equations of I and II Type and Their Connections with Finite Equations of Motion and the Callan-Symanzik Equation.- Nelson's Symmetry at Work: The Infinite Volume Behavior of the Vacuum for Two-Dimensional Self-Coupled Bose Fields.- Path Integrals and Gauge Theories.- Renormalizable Models with Broken Symmetries.- Group Theoretical Approach to Conformal Invariant Quantum Field Theory.- Use of Invariant Transformations in Problems of Superconductivity.- Analytic Renormalization of the a-Model.- Recent Progress on Computational Methods in Field Theory.- Short Review of Small-Distance-Behaviour Analysis.- Diagrammar and Dimensional Renormalization.- Quantum Gravity as a Gauge Field Theory.- Self-Consistent Quantum Field Theory and Symmetry Breaking.- The Present Status of the Computing Methods in Quantum Electrodynamics.- Relativistic Strings and Supergauges.- Application of Gauge Theories to Weak and Electromagnetic Interactions.