Quantum Topology And Global Anomalies (advanced Series In Mathematical Physics)
by R A Baadhio /
1996 / English / DjVu
3.8 MB Download
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.
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.