Geometric Methods for Quantum Field Theory

Geometric Methods for Quantum Field Theory
ISBN-10
9814492825
ISBN-13
9789814492829
Category
Science
Pages
528
Language
English
Published
2001-04-30
Publisher
World Scientific
Authors
Hernan Ocampo, Sylvie Paycha, Andres Reyes

Description

Both mathematics and mathematical physics have many active areas of research where the interplay between geometry and quantum field theory has proved extremely fruitful. Duality, gauge field theory, geometric quantization, Seiberg–Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups offer some striking recent examples of modern topics which stand on the borderline between geometry and analysis on the one hand and quantum field theory on the other, where the physicist's and the mathematician's perspective complement each other, leading to new mathematical and physical concepts and results. This volume introduces the reader to some basic mathematical and physical tools and methods required to follow the recent developments in some active areas of mathematical physics, including duality, gauge field theory, geometric quantization, Seiberg-Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups. It comprises seven self-contained lectures, which should progressively give the reader a precise idea of some of the techniques used in these areas, as well as a few short communications presented by young participants at the school. Contents:Lectures:Introduction to Differentiable Manifolds and Symplectic Geometry (T Wurzbacher)Spectral Properties of the Dirac Operator and Geometrical Structures (O Hijazi)Quantum Theory of Fermion Systems: Topics Between Physics and Mathematics (E Langmann)Heat Equation and Spectral Geometry. Introduction for Beginners (K Wojciechowski)Renormalized Traces as a Geometric Tool (S Paycha)Concepts in Gauge Theory Leading to Electric-Magnetic Duality (T S Tsun)An Introduction to Seiberg-Witten Theory (H Ocampo)Short Communications:Remarks on Duality, Analytical Torsion and Gaussian Integration in Antisymmetric Field Theories (A Cardona)Multiplicative Anomaly for the ς-Regularized Determinant (C Ducourtioux)On Cohomogeneity One Riemannian Manifolds (S M B Kashani)A Differentiable Calculus on the Space of Loops and Connections (M Reiris)Quantum Hall Conductivity and Topological Invariants (A Reyes)Determinant of the Dirac Operator Over the Interval [0,β] (F Torres-Ardila) Readership: Mathematicians and physicists. Keywords:Reviews:“Many texts in theoretical physics do not contain a rigorous account of the mathematics they employ. However, this text does, and it omits no steps in the logic, thus making it very accessible to the mathematical community. Also it emphasizes physics, providing a link between the two disciplines which one rarely finds in a text.”Contemporary Physics

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