Constructive Quantum Field Theory II

✍ Scribed by A. S. Wightman (auth.), G. Velo, A. S. Wightman (eds.)

• Publisher: Springer US
• Year: 1990
• Tongue: English
• Leaves: 343
• Series: NATO ASI Series 234
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-viii
Remarks on What We Have Learned....Pages 1-14
Renormalization Group....Pages 15-53
Constructive Gauge Theory II....Pages 55-68
The Beta-Function Method for Resummations in Field Theory....Pages 69-88
Wess-Zumino-Witten Conformal Field Theory....Pages 89-120
Two-Dimensional Conformal Field Theory and Three-Dimensional Topology....Pages 121-199
Renormalization Theory and the Tree Expansion....Pages 201-233
Critical Properties of Some Discrete Random Surface Models....Pages 235-264
Quantum Physics and Gravitation....Pages 265-282
Geometry of Supersymmetry....Pages 283-305
Conformal Field Theory in String Theory....Pages 307-325
Multiparticle Structure and Wilson Short-Distance Expansion in Field Theories....Pages 327-328
Various Aspects of the Bethe-Salpeter Structure in Quantum Field Theory....Pages 329-330
Supersymmetry Breaking in Wess-Zumino Models....Pages 331-331
First Order Phase Transitions in Large N Lattice Higgs Models and Pirogov Sinai Theory....Pages 333-335
The Coleman-Weinberg Mechanism in the Abelian Lattice Higgs Model....Pages 337-337
Quantum Solitons....Pages 339-341
Back Matter....Pages 343-344

✦ Subjects

Theoretical, Mathematical and Computational Physics