Differential Geometrical Methods in Theoretical Physics

M. Werner

ISBN 10: 9027728208 / ISBN 13: 9789027728203

Published by Springer Netherlands, Springer Netherlands, 1988

About this Item

Druck auf Anfrage Neuware - Printed after ordering - After almost half a century of existence the main question about quantum field theory seems still to be: what does it really describe and not yet: does it provide a good description of nature J. A. Swieca Ever since quantum field theory has been applied to strong int- actions, physicists have tried to obtain a nonperturbative und- standing. Dispersion theoretic sum rules, the S-matrix bootstrap, the dual models (and their reformulation in string language) and s the conformal bootstrap of the 70 are prominent cornerstones on this thorny path. Furthermore instantons and topological solitons have shed some light on the nonperturbati ve vacuum structure respectively on the existence of nonperturbative 'charge' s- tors. To these attempts an additional one was recently added', which is yet not easily describable in terms of one 'catch phrase'. Dif- rent from previous attempts, it is almost entirely based on new noncommutative algebraic structures: 'exchange algebras' whose 'structure constants' are braid matrices which generate a ho- morphism of the infini te (inducti ve limi t) Artin braid group Boo into a von Neumann algebra. Mathematically there is a close 2 relation to recent work of Jones Its physical origin is the resul t of a subtle analysis of Ei nstein causality expressed in terms of local commutati vi ty of space-li ke separated fields. It is most clearly recognizable in conformal invariant quantum field theories.

Seller Inventory # 9789027728203

Bibliographic Details

• Title: Differential Geometrical Methods in Theoretical Physics
• Publisher: Springer Netherlands, Springer Netherlands
• Publication Date: 1988
• Language: English
• ISBN 10: 9027728208
• ISBN 13: 9789027728203
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 31D millimeters 241 millimeters width by 160 millimeters height by 31 millimeters depth
• Weight: 898 grams

About this title

Synopsis

After almost half a century of existence the main question about quantum field theory seems still to be: what does it really describe? and not yet: does it provide a good description of nature? J. A. Swieca Ever since quantum field theory has been applied to strong int- actions, physicists have tried to obtain a nonperturbative und- standing. Dispersion theoretic sum rules, the S-matrix bootstrap, the dual models (and their reformulation in string language) and s the conformal bootstrap of the 70 are prominent cornerstones on this thorny path. Furthermore instantons and topological solitons have shed some light on the nonperturbati ve vacuum structure respectively on the existence of nonperturbative "charge" s- tors. To these attempts an additional one was recently added', which is yet not easily describable in terms of one "catch phrase". Dif- rent from previous attempts, it is almost entirely based on new noncommutative algebraic structures: "exchange algebras" whose "structure constants" are braid matrices which generate a ho- morphism of the infini te (inducti ve limi t) Artin braid group Boo into a von Neumann algebra. Mathematically there is a close 2 relation to recent work of Jones - Its physical origin is the resul t of a subtle analysis of Ei nstein causality expressed in terms of local commutati vi ty of space-li ke separated fields. It is most clearly recognizable in conformal invariant quantum field theories.

Review

`Anybody ... will find in this book a lot of new original information and inspiration for further research.'
Class Quantum Grav, 7, 1990