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© 2000

Equivariant Cohomology and Localization of Path Integrals

Book

Part of the Lecture Notes in Physics Monographs book series (LNPMGR, volume 63)

About this book

Introduction

This book, addressing both researchers and graduate students, reviews equivariant localization techniques for the evaluation of Feynman path integrals. The author gives the relevant mathematical background in some detail, showing at the same time how localization ideas are related to classical integrability. The text explores the symmetries inherent in localizable models for assessing the applicability of localization formulae. Various applications from physics and mathematics are presented.

Keywords

Cohomological Quantum Field Theory Duistermaat-Heckman Theorem Equivariant Cohomology Feynman Path Integral Lie Groups Localization Techniques Morse Theory Quantum Integrability Quantum mechanics Semi-classical Approximation Topological Quantum Field Theory cohomology group theory homology

Authors and affiliations

  1. 1.The Niels Bohr InstituteCopenhagen ØDenmark
  2. 2.Department of Physics - Theoretical PhysicsUniversity of OxfordOxfordUK

Bibliographic information

Reviews

"A thorough exposition of the current state of applying equivariant cohomology to quantum field theory. [...] If one takes the attitude that this material may make mathematical sense within the next fifty years, the book can be appreciated as a well-organized exposition of the topological content of quantum field theory from a physics viewpoint." (Mathematical Reviews 2002a)