Quantum theories and geometry. Based on lectures given at a meeting held at the Fondation Les Treilles, France, March 23-27, 1987
type: Item
instance of: scholarly article
title: Quantum theories and geometry. Based on lectures given at a meeting held at the Fondation Les Treilles, France, March 23-27, 1987
zbMATH Open document ID: 0688.53032
published in: Mathematical Physics Studies
publication date: 1993-06-05T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53B50
Mathematics Subject Classification ID: 53-06
Mathematics Subject Classification ID: 83-06
Mathematics Subject Classification ID: 81-06
zbMATH DE Number: 193551
zbMATH Keywords: Quantum theories
zbMATH Keywords: Geometry
zbMATH Keywords: Meeting
zbMATH Keywords: Lectures
zbMATH Keywords: Les Treilles (France)
zbMATH Keywords: Schwinger terms
zbMATH Keywords: commutation or anticommutation relations
zbMATH Keywords: deformation theory
zbMATH Keywords: brackets
zbMATH Keywords: quantization
zbMATH Keywords: statistical mechanics
zbMATH Keywords: conformal invariant electrodynamics
zbMATH Keywords: quantized general relativity
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: spherical pendelum
zbMATH Keywords: Schwarzian derivative
zbMATH Keywords: harmonic maps
zbMATH Keywords: K- flows
reviewed by: A. O. Barut
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 193551