Recent Developments in Gauge Theories

1. Front Matter

   Pages i-viii

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2. Remarks on Morse Theory

   • M. F. Atiyah

   Pages 1-5

3. Morse Theoretic Aspects of Yang-Mills Theory

   • Raoul Bott

   Pages 7-28

4. A Semiclassical Approach to the Strong Coupling Physics of QCD

   • Curtis G. Callan Jr.

   Pages 29-44

5. Lattice Gauge Theories

   • James Glimm

   Pages 45-52

6. Some Results and Comments on Quantized Gauge Fields

   • Jürg Fröhlich

   Pages 53-82

7. String States in Q.C.D.

   • Jean-Loup Gervais, André Neveu

   Pages 83-99

8. Why do We Need Local Gauge Invariance in Theories with Vector Particles? An Introduction

   • G.’t Hooft

   Pages 101-115

9. Which Topological Features of a Gauge Theory can be Responsible for Permanent Confinement?

   • G.’t Hooft

   Pages 117-133

10. Naturalness, Chiral Symmetry, and Spontaneous Chiral Symmetry Breaking

    • G.’t Hooft

    Pages 135-157

11. Introduction to Lattice Gauge Theories

    • C. Itzykson

    Pages 159-188

12. Classical Gauge Theories and Their Quantum Role

    • Arthur Jaffe

    Pages 189-200

13. The Coupling Constant in a φ4 Field Theory

    • James Glimm, Arthur Jaffe

    Pages 201-204

14. Exact Instanton Gases

    • M. Lüscher

    Pages 205-216

15. Properties of Lattice Gauge Theory Models at Low Temperatures

    • Gerhard Mack

    Pages 217-263

16. Geometry of the Space of Gauge Orbits and the Yang-Mills Dynamical System

    • P. K. Mitter

    Pages 265-292

17. On the Structure of the Phases in Lattice Gauge Theories

    • Giorgio Parisi

    Pages 293-301

18. Superalgebras and Confinement in Condensed Matter Physics

    • V. Poénaru

    Pages 303-311

19. Cutoff Dependence in Lattice ø 4 4 Theory

    • K. Symanzik

    Pages 313-330

20. Gauge Concepts in Condensed Matter Physics

    • Gérard Toulouse

    Pages 331-362

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.

• Confinement
• Lattice gauge theory
• Particle Physics
• Phase
• Quark
• mechanics

• Institute for Theoretical Physics, Utrecht, The Netherlands

  G.’t Hooft

• CEN Saclay, Gif-sur-Yvette, France

  C. Itzykson

• Harvard University, Cambridge, USA

  A. Jaffe

• University of Hamburg, Hamburg, Federal Republic of Germany

  H. Lehmann

• University of Paris, Paris, France

  P. K. Mitter

• University of California, Berkeley, USA

  I. M. Singer

• Center of Theoretical Physics, CNRS, Marseille, France

  R. Stora

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