Quantum theories and geometry. Based on lectures given at a meeting held at the Fondation Les Treilles, France, March 23-27, 1987 (Q1210833)

The articles of this volume will not be indexed individually. Modern geometrical methods found in recent years many interesting applications in Theoretical Physics, in particular in gauge field theories, quantization and particle physics. This book collects 10 articles, ordered alphabetically, by physicists and mathematicians on the following topics of mathematical physics. Araki discusses the identification of Schwinger terms in the canonical commutation or anticommutation relations of field theory with cyclic 1-cycles. The contributions by Arnal, Gutt and Lichnerowicz are devoted to the deformation theory of brackets and quantization, and the associated *- products. Lichnerowicz' paper is a very original application of deformations to statistical mechanics with the deformation parameter being the inverse temperature. Two papers are on constructing field theories, one by Flato, Fronsdal and Sternheimer for conformal invariant electrodynamics, the other by Haag on the difficulties of quantized general relativity. Duistermaat discusses the Schrödinger operator for spherical pendelum, Kostant and Sternberg the geometrical interpretation of Schwarzian derivative and J. Rawsley harmonic maps of a Riemann surface in a symmetric space. Finally Misra and Antoniou write about the implications of irreversibilty and the properties of K-flows.