Ebook: Recent Developments in Gauge Theories

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.

---

---

Content:
Front Matter....Pages i-viii
Remarks on Morse Theory....Pages 1-5
Morse Theoretic Aspects of Yang-Mills Theory....Pages 7-28
A Semiclassical Approach to the Strong Coupling Physics of QCD....Pages 29-44
Lattice Gauge Theories....Pages 45-52
Some Results and Comments on Quantized Gauge Fields....Pages 53-82
String States in Q.C.D.....Pages 83-99
Why do We Need Local Gauge Invariance in Theories with Vector Particles? An Introduction....Pages 101-115
Which Topological Features of a Gauge Theory can be Responsible for Permanent Confinement?....Pages 117-133
Naturalness, Chiral Symmetry, and Spontaneous Chiral Symmetry Breaking....Pages 135-157
Introduction to Lattice Gauge Theories....Pages 159-188
Classical Gauge Theories and Their Quantum Role....Pages 189-200
The Coupling Constant in a ?4 Field Theory....Pages 201-204
Exact Instanton Gases....Pages 205-216
Properties of Lattice Gauge Theory Models at Low Temperatures....Pages 217-263
Geometry of the Space of Gauge Orbits and the Yang-Mills Dynamical System....Pages 265-292
On the Structure of the Phases in Lattice Gauge Theories....Pages 293-301
Superalgebras and Confinement in Condensed Matter Physics....Pages 303-311
Gauge Concepts in Condensed Matter Physics....Pages 313-330
Monte-Carlo Calculations for the Lattice Gauge Theory....Pages 331-362
The 1/N Expansion in Atomic and Particle Physics....Pages 363-402
Generalized Non-Linear ?-Models with Gauge Invariance....Pages 403-419
Back Matter....Pages 421-436
....Pages 437-438