Almost all theories of fundamental interactions are nowadays based on the gauge concept. Starting with the historical example of quantum electrodynamics, we have been led to the successful unified gauge theory of weak and electromagnetic interactions, and finally to a non abelian gauge theory of strong interactions with the notion of permanently confined quarks. The. early theoretical work on gauge theories was devoted to proofs of renormalizability, investigation of short distance behaviour, the discovery of asymptotic freedom, etc . . , aspects which were accessible to tools extrapolated from renormalised perturbation theory. The second phase of the subject is concerned with the problem of quark confinement which necessitates a non-perturbative understanding of gauge theories. This phase has so far been marked by the introduc­ tion of ideas from geometry, topology and statistical mechanics in particular the theory of phase transitions. The 1979 Cargese Institute on "Recent Developments on Gauge Theories" was devoted to a thorough discussion of these non-perturbative, global aspects of non-abelian gauge theories. In the lectures and seminars reproduced in this volume the reader wilf find detailed reports on most of the important developments of recent times on non perturbative gauge fields by some of the leading experts and innovators in this field. Aside from lectures on gauge fields proper, there were lectures on gauge field concepts in condensed matter physics and lectures by mathematicians on global aspects of the calculus of variations, its relation to geometry and topology, and related topics.

Inhalt

Remarks on Morse Theory.- Morse Theoretic Aspects of Yang-Mills Theory.- A Semiclassical Approach to the Strong Coupling Physics of QCD.- Lattice Gauge Theories.- Some Results and Comments on Quantized Gauge Fields.- String States in Q C D.- Why Do We Need Local Gauge Invariance in Theories with Vector Particles? An Introduction. (Lecture I).- Which Topological Features of a Gauge Theory can be Responsible for Permanent Confinement? (Lecture II).- Naturalness, Chiral Symmetry, and Spontaneous Chiral Symmetry Breaking. (Lecture III).- to Lattice Gauge Theories.- Classical Gauge Theories and Their Quantum Role.- The Coupling Constant in a Ø4 Field Theory.- Exact Instanton Gases.- Properties of Lattice Gauge Theory Models at Low Temperatures.- Geometry of the Space of Gauge Orbits and the Yang-Mills Dynamical System.- On the Strgcture of the Phases in Lattice Gauge Theories.- Superalgebras and Confinement in Condensed Matter Physics.- Cutoff Dependence in Lattice $$ {\mathop \phi \limits_4 ^4}$$ Theory.- Gauge Concepts in Condensed Matter Physics.- Monte-Carlo Calculations for the Lattice Gauge Theory.- The 1/N Expansion in Atomic and Particle Physics.- Generalized Non-Linear a-Models with Gauge Invariance.