Constructive Quantum Field Theory II

1. Front Matter

   Pages i-viii

   PDF

2. Constructive Quantum Field Theory from I to II

   1. Remarks on What We Have Learned

      • A. S. Wightman

      Pages 1-14

   2. Renormalization Group

      • Roland Seneor

      Pages 15-53

   3. Constructive Gauge Theory II

      • T. Balaban

      Pages 55-68

   4. The Beta-Function Method for Resummations in Field Theory

      • Giovanni Gallavotti

      Pages 69-88

   5. Wess-Zumino-Witten Conformal Field Theory

      • Krzysztof Gawędzki

      Pages 89-120

   6. Two-Dimensional Conformal Field Theory and Three-Dimensional Topology

      • J. Fröhlich, C. King

      Pages 121-199

   7. Renormalization Theory and the Tree Expansion

      • Lon Rosen

      Pages 201-233

   8. Critical Properties of Some Discrete Random Surface Models

      • Bergfinnur Durhuus

      Pages 235-264

   9. Quantum Physics and Gravitation

      • Rudolf Haag

      Pages 265-282

   10. Geometry of Supersymmetry

       • Arthur Jaffe, Andrzej Lesniewski

       Pages 283-305

   11. Conformal Field Theory in String Theory

       • Jeffrey A. Harvey

       Pages 307-325

3. Seminars

   1. Multiparticle Structure and Wilson Short-Distance Expansion in Field Theories

      • D. Iagolnitzer

      Pages 327-328

   2. Various Aspects of the Bethe-Salpeter Structure in Quantum Field Theory

      • J. Bros

      Pages 329-330

   3. Supersymmetry Breaking in Wess-Zumino Models

      • John Z. Imbrie

      Pages 331-331

   4. First Order Phase Transitions in Large N Lattice Higgs Models and Pirogov Sinai Theory

      • Christian Borgs

      Pages 333-335

   5. The Coleman-Weinberg Mechanism in the Abelian Lattice Higgs Model

      • Florian Nill

      Pages 337-337

   6. Quantum Solitons

      • P. A. Marchetti

      Pages 339-341

4. Back Matter

   Pages 343-344

   PDF

The seventh Ettore Majorana International School of Mathematical Physics was :Jeld at the Centro della Cultura Scientifica Erice. Sicily, 1-15 July 1988. The present volume collects lecture notes on the session which was entitled Con8tructive Quantum Field Theory lI. The II refers to the fact that the first such school in 1973 was devoted ,0 the same subject. The school was a NATO Advanced Study Institute sponsored Jy the Italian Ministry of Scientific and Technological Research and the Regional 3icilian Government. At the time of the 1973 Erice School on Constructive Field Theory, the speakers :ould summarize a decade of effort on the solution of superrenormalizable models in two dimensional space-time leading to the verification of the axioms of relativistic :J. uantum field theory for these examples. The resulting lecture notes have proved ,0 be exceptionally useful and are still in print. In the decade and a half that have ~lapsed since that time, there has been much hard work with the ultimate objective of providing a rigorous mathematical foundation for the quantum field theories in four iimensional space-time that summarize a large fraction of our current understanding )f elementary particle physics: QCD and the electroweak theory. The lecture notes )f the 1988 school record the fact that, although this objective has not been reached, Important progress has been made. The ultraviolet stability of Yang-Mills theory In four dimensions has been treated and renormalizable (not superrenormalizable) models in two dimensional space-time, Gross-Neveu models, have been solved.

• Gauge theory
• Renormalization group
• Soliton
• geometry
• linear optimization
• mathematical physics
• model
• verification

• University of Bologna, Bologna, Italy

  G. Velo

• Princeton University, Princeton, USA

  A. S. Wightman

Policies and ethics