Geometric and Topological Methods for Quantum Field Theory

by Edited by Hernan Ocampo , Eddy Pariguan , Sylvie Paycha

• ISBN13: 9780521764827
• ISBN10: 0521764823
• Edition: 1st
• Format: Hardcover
• Copyright: 2010-06-07
• Publisher: Cambridge University Press

Summary

Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest.

Author Biography

Hernan Ocampo is a Professor of Theoretical Physics atthe University del valle, Cali, Colombia.
Eddy Pariguan is an Associate Professor in Mathematics atthe University La javeriana, Bogota, Colombia.
Sylvie paycha is a Professor of Mathematics at the university Blaise Pascal, Clermont-Ferrand, France.

Table of Contents

List of contributors	p. ix
Introduction	p. xi
The impact of QFT on low-dimensional topology	p. 1
Differential equations aspects of quantum cohomology	p. 54
Index theory and groupoids	p. 86
Renormalization Hopf algebras and combinatorial groups	p. 159
BRS invariance for massive boson fields	p. 220
Large-N field theories and geometry	p. 253
Functional renormalization group equations, asymptotic safety, and quantum Einstein gravity	p. 288
When is a differentiable manifold the boundary of an orbifold?	p. 330
Canonical group quantization, rotation generators, and quantum indistinguishability	p. 344
Conserved currents in Kähler manifolds	p. 368
A symmetrized canonical determinant on odd-class pseudodifferential operators	p. 381
Some remarks about cosymplectic metrics on maximal flag manifolds	p. 394
Heisenberg modules over real multiplication noncommutative tori and related algebraic structures	p. 405
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