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Full Description
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.
Contents
Constructive Quantum Field Theory from I to II.- Remarks on What We have Learned.- Renormalization Group.- Constructive Gauge Theory II.- The Beta-Function Method for Resummations in Field Theory.- Wess-Zumino-Witten Conformal Field Theory.- Two-Dimensional Conformal Field Theory and Three-Dimensional Topology.- Renormalization Theory and the Tree Expansion.- Critical Properties of Some Discrete Random Surface Models.- Quantum Physics and Gravitation.- Geometry of Supersymmetry.- Conformal Field Theory in String Theory.- Seminars.- Multiparticle Structure and Wilson Short-Distance Expansion in Field Theories.- Various Aspects of the Bethe-Salpeter Structure in Quantum Field Theory.- Supersymmetry Breaking in Wess-Zumino Models.- First Order Phase Transition in Large N Lattice Higgs Models and Pirogov Sinai Theory.- The Coleman-Weinberg Mechanism in the Abelian Lattice Higgs Model.- Quantum Solitons.
