Geometric Analysis and Applications to Quantum Field Theory

Geometric Analysis and Applications to Quantum Field Theory

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Overview

Geometric Analysis and Applications to Quantum Field Theory by Peter Bouwknegt

In recent years, there has been tremendous progress on the interface of geometry and mathematical physics. This book reflects the expanded articles of several lectures in these areas delivered at the University of Adelaide, with an audience of primarily graduate students.
The aim of this volume is to provide surveys of recent progress without assuming too much prerequisite knowledge and with a comprehensive bibliography, so that researchers and graduate students in geometry and mathematical physics will benefit.
The contributors cover a number of areas in mathematical physics.
Chapter 1 offers a self-contained derivation of the partition function of Chern-Simons gauge theory in the semiclassical approximation.
Chapter 2 considers the algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory, including their relation to the braid group, quantum groups and infinite dimensional Lie algebras.
Chapter 3 surveys the application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems.
Chapter 4 examines the variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds.
Chapter 5 is a review of monopoles in non-Abelian gauge theories and the various approaches to understanding them.
Chapter 6 covers much of the exciting recent developments in quantum cohomology, including relative Gromov-Witten invariant, birational geometry, naturality and mirror symmetry.
Chapter 7 explains the physics origin of the Seiberg-Witten equations in four-manifold theory and a number of important concepts inquantum field theory, such as vacuum, mass gap, (super)symmetry, anomalies and duality.
Contributors: D.H. Adam, P. Bouwknegt, A.L. Carey, A. Harris, E. Langmann, M.K. Murray, Y. Ruan, S. Wu
D. H. Adams: Semiclassical Approximation in Chern-Simons Gauge Theory
P. Bouwknegt: The Knizhnik-Zamolodchikov Equations
A. L. Carey and E. Langmann: Loop Groups and Quantum Fields
A. Harris: Some Applications of Variational Calculus in Hermitian Geometry
M. K. Murray: Monopoles
Y. Ruan: On Gromov-Witten Invariants and Quantum Cohomology
S. Wu The Geometry and Physics of the Seiberg-Witten Equations

Product Details

ISBN-13: 9781461265979
Publisher: Birkh�user Boston
Publication date: 11/01/2012
Series: Progress in Mathematics , #205
Edition description: Softcover reprint of the original 1st ed. 2002
Pages: 207
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Preface
Semiclassical Approximation in Chern-Simons Guage Theory
The Knizhnik-Zamolodchikov Equations
Loop Groups and Quantum Fields
Some Applications of Variational Calculus in Hermitian Geometry
Monopoles
Gromov-Witten Invariants and Quantum Cohomology
The Geometry and Physics of the Seiberg-Witten Equations

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