Geometric and Topological Methods for Quantum Field Theory: Proceedings of the 2009 Villa de Leyva Summer School

doi:10.1017/CBO9781139208642

Based on lectures given at the renowned Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory methods and their applications to quantum field theory, the book covers topics such as Dirac structures, holomorphic bundles and stability, Feynman integrals, geometric aspects of quantum field theory and the standard model, spectral and Riemannian geometry and index theory. This is a valuable guide for graduate students and researchers in physics and mathematics wanting to enter this interesting research field at the borderline between mathematics and physics.

'… a valuable guide for graduate students and researchers in physics and mathematics …'

Source: CERN Courier

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Contents

Frontmatter
pp i-iv
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Contents
pp v-viii
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List of contributors
pp ix-x
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Introduction
pp 1-3
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1 - A brief introduction to Dirac manifolds
pp 4-38
- By Henrique Bursztyn, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brasil
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2 - Differential geometry of holomorphic vector bundles on a curve
pp 39-80
- By Florent Schaffhauser, Universidad de los Andes
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3 - Paths towards an extension of Chern–Weil calculus to a class of infinite dimensional vector bundles
pp 81-143
- By Sylvie Paycha, Universität Potsdam
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4 - Introduction to Feynman integrals
pp 144-187
- By Stefan Weinzierl, Universität Mainz
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5 - Iterated integrals in quantum field theory
pp 188-240
- By Francis Brown, CNRS – Institut de Mathématiques de Jussieu, Paris, France
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6 - Geometric issues in quantum field theory and string theory
pp 241-273
- By Luis J. Boya, Universidad de Zaragoza
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7 - Geometric aspects of the Standard Model and the mysteries of matter
pp 274-306
- By Florian Scheck, Johannes Gutenberg–University
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8 - Absence of singular continuous spectrum for some geometric Laplacians
pp 307-321
- By Leonardo A. Cano García, Universidad de los Andes
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9 - Models for formal groupoids
pp 322-339
- By Iván Contreras, Universität Zürich
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10 - Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity
pp 340-365
- By Andrés Vargas, Pontificia Universidad Javeriana
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11 - Regularized traces and the index formula for manifolds with boundary
pp 366-380
- By Alexander Cardona, Universidad de los Andes, César Del Corral, Universidad de los Andes
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Index
pp 381-383
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Geometric and Topological Methods for Quantum Field Theory

Proceedings of the 2009 Villa de Leyva Summer School

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

List of contributors
pp ix-x

Introduction
pp 1-3

1 - A brief introduction to Dirac manifolds
pp 4-38

2 - Differential geometry of holomorphic vector bundles on a curve
pp 39-80

3 - Paths towards an extension of Chern–Weil calculus to a class of infinite dimensional vector bundles
pp 81-143

4 - Introduction to Feynman integrals
pp 144-187

5 - Iterated integrals in quantum field theory
pp 188-240

6 - Geometric issues in quantum field theory and string theory
pp 241-273

7 - Geometric aspects of the Standard Model and the mysteries of matter
pp 274-306

8 - Absence of singular continuous spectrum for some geometric Laplacians
pp 307-321

9 - Models for formal groupoids
pp 322-339

10 - Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity
pp 340-365

11 - Regularized traces and the index formula for manifolds with boundary
pp 366-380

Index
pp 381-383

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Geometric and Topological Methods for Quantum Field Theory

Proceedings of the 2009 Villa de Leyva Summer School

Book description

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Contents

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Accessibility standard: Unknown

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