Quantum topology and global anomalies
Author(s)
Bibliographic Information
Quantum topology and global anomalies
（Advanced series in mathematical physics / editors-in-charge, D.H. Phong, S.-T. Yan, v. 23）
World Scientific, c1996
- : hard
- : pbk
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Note
Includes bibliographical references and index
Description and Table of Contents
- Volume
-
: hard ISBN 9789810227265
Description
Anomalies are ubiquitous features in quantum field theories. They can ruin the consistency of such theories and put significant restrictions on their viability, especially in dimensions higher than four. Global gauge and gravitational anomalies are to date, one of the scant powerful and probing tools available to physicists in the pursuit of uniqueness.This monograph is one of the very few that specializes in the study of global anomalies in quantum field theories. A discussion of various issues associated to three dimensional physics — the Chern-Simons-Witten theories — widen the scope of this book. Topics discussed here comprises: the ongoing quest for three-manifolds invariant, the role of the mapping class groups in (a) the detection and cancellation of global anomalies, (b) formulating three-manifolds invariant; the geometric quantization of Chern-Simons-Witten theories; deformation quantization; study of chiral and gravitational anomalies; anomalies and the Atiyah-Patodi-Singer Index theorem; exotic spheres; global gravitational anomalies in some six and ten dimensional supergravity and superstring theories, with an additional case study of Witten SU(2) Global Gauge Anomalies.In addition, five chapters lay out the mathematical basis for a thorough use of the topics above. One chapter focuses on the relationship between Teichmüller spaces, moduli spaces and mapping class groups. Another chapter is devoted to mapping class groups and arithmetic groups. Gauge theories on Riemann surfaces are studies in well over two chapters, the first one centered on the theory of bundles and the second on connections.Many readers will find this a useful book, especially theoretical physicists and mathematicians. The material presented here will be of interest to both the experts who will find complete, detailed and precise descriptions of important topics of current interest in mathematical physics, and to students and newcomers to the field, who will appreciate the vast amount of information provided here, especially on global anomalies.
Table of Contents
- The ongoing quest for three-manifold invariants
- mapping class groups
- mapping class groups and arithmetic groups
- Weil-Petersson geometry of Teichmuller spaces
- gauge theories on Reimann surfaces I
- bundles
- gauge theories on Reimann surfaces II
- connections
- geometric quantization of Chern-Simons-Witten theories
- deformation quantization
- chiral and gravitational anomalies
- anomalies and the index theorem
- global anomalies
- exotic spheres.
- Volume
-
: pbk ISBN 9789810227272
Description
A discussion of various issues associated to three-dimensional physics, the Chern-Simons-Witten theories aim to widen the scope of this text. Topics include anomalies and the Atiyah-Patodi-Singer Index theorem, exotic spheres, and the geometric quantization of Chern-Simons-Witten theories.
by "Nielsen BookData"