Nonperturbative Quantum Field Theory - Hooft, G.; Jaffe, A.; Mack, G.; Mitter, P. K.; Stora, R. (Springer US, 1988)
During the past 15 years, quantum field theory and classical statistical mechanics have merged into a single field, and the need for nonperturbative methods for the description of critical phenomena in statistical mechanics as well as for problems in elementary particle physics are generally acknowledged. Such methods formed the central theme of the 1987 Cargese Advanced Study Institute on "Nonperturbative Quantum Field Theory. " The use of conformal symmetry has been of central interest in recent years, and was a main subject at the ASI. Conformal invariant quantum field theory describes statistical mechanical systems exactly at a critical point, and can be analysed to a remarkable extent by group theoretical methods. Very strong results have been obtained for 2-dimensional systems. Conformal field theory is also the basis of string theory, which offers some hope of providing a unified theory of all interactions between elementary particles. Accordingly, a number of lectures and seminars were presented on these two topics. After systematic introductory lectures, conformal field theory on Riemann surfaces, orbifolds, sigma models, and application of loop group theory and Grassmannians were discussed, and some ideas on modular geometry were presented. Other lectures combined traditional techniques of constructive quantum field theory with new methods such as the use of index-theorems and infinite dimensional (Kac Moody) symmetry groups. The problems encountered in a quantum mechanical description of black holes were discussed in detail