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Geometric methods for quantum field theory : proceedings of the summer school : Villa de Leyva, Colombia, 12-30 July 1999 / editors, Hernan Ocampo, Sylvie Paycha, Andres Reyes

Additional Titles
Proceedings of the summer school, geometric methods for quantum field theory
Published
Singapore ; River Edge, N.J. : World Scientific, [2001]
Copyright Date
©2001
Physical Description
1 online resource (vii, 520 pages) : illustrations
Additional Creators
Ocampo, Hernan, Paycha, Sylvie, and Reyes, Andrés
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Language Note
English.
Contents
Introduction -- Lectures. Lecture 1: Introduction to differentiable manifolds andsymplectic geometry /Tilmann Wurzbacher -- Lecture 2: Spectral properties of the Dirac operator and geometrical structures / Oussama Hijazi -- Lecture 3: Quantum theory of fermion systems: topics between physics and mathematics / Edwin Langmann -- Lecture 4: Heat equation and spectral geometry. Introduction for beginners / Krzysztof Wojciechowski -- Lecture 5: Renormalized traces as a geometric tool /Sylvie Paycha -- Lecture 6: Concepts in gauge theory leading to electricmagnetic duality / Tsou Sheung Tsun -- Lecture 7: An introduction to Seiberg-Witten theory /Hernan Ocampo -- Short communications. Remarks on duality, analytic torsion and Gaussian integration in antisymmetric field theories / Alexander Cardona -- Multiplicative anomaly for the [symbol]-regularized determinant / Catherine Ducourtioux -- On cohomogeneity one Riemannian manifolds / S.M.B. Kashani -- A differentiable calculus on the space of loops and connections / Martin Reiris -- Quantum Hall conductivity and topological invariants / Andres Reyes -- Determinant of the Dirac operator over the interval [symbol] / Fabian Torres-Ardila.
Summary
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, Sieberg-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 betwen 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, Sieberg-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 and the school.
Subject(s)
Genre(s)
ISBN
9789812810571 (electronic bk.)
9812810579 (electronic bk.)
1281956252
9781281956255
9789810243517
9810243510
9786611956257
6611956255
Digital File Characteristics
data file
Bibliography Note
Includes bibliographical references.
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