Renormalization Theory

The present volume collects lecture notes from the session of the International School of Mathematical Physics 'Ettore Majorana' on Renormalization Theory that took place in Erice (Sicily), August 17 to August 31, 1975. The School was a NATO Advanced Study Institute sponsored by the Italian Ministry of Public Education, the Italian Minis­ try of Scientific and Technological Research, and the Regional Sicilian Government. Renormalization theory has, by now, acquired forty years of history. The present volume assumes a general acquaintance with the elementary facts of the subject as they might appear in an introductory course in quantum field theory. For more recent significant developments it provides a systematic intro­ duction as well as a detailed discussion of the existing state of knowledge. In particular analytic and dimensional renorma­ lization, normal product technique, and the Bogoliubov-Shirkov­ Epstein-Glaser method are treated, with applications to physically important gauge theories. All the preceding deals with perturbative renormalization theory. In recent years there has been an interesting development of non-perturbative renormalization theory in models in space-times of two and three dimensions, with the use of the methods of constructive field theory. Despite the simplicity of these models, the results are of significance because they are exact and answer a number of questions of principle. There are parts of renormalization theory which are not well understood, for instance the renormalization theory of non-renormalizable interactions.

Contenu

Orientation.- Dimensional and Analytic Renormalization.- BPHZ Renormalization.- Remark on Equivalent Formulations for Bogoliubov's Method of Renormalization.- The Power Counting Theorem for Feynman Integrals with Massless Propagators.- Some Results on Dimensional Renormalization.- Adiabatic Limit in Perturbation Theory.- Existence of Green's Functions in Perturbative Q.E.D..- Gauge Field Models.- Renormalizable Models with Broken Symmetries.- Renormalized Perturbation Theory: Achievements, Limitations and Open Problems.- Quantum Sine-Gordon Equation and Quantum Solitons in Two Space-Time Dimensions.- Non-Perturbative Renormalization in the Yukawa Model in Two Dimensions.- The Non-Perturbative Renormalization of (? ?4)3.- Non-Renormalizable Quantum Field Theories.