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

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.

Introduction; 1. A brief introduction to Dirac manifolds Henrique Bursztyn; 2. Differential geometry of holomorphic vector bundles on a curve Florent Schaffhauser; 3. Paths towards an extension of Chern–Weil calculus to a class of infinite dimensional vector bundles Sylvie Paycha; 4. Introduction to Feynman integrals Stefan Weinzierl; 5. Iterated integrals in quantum field theory Francis Brown; 6. Geometric issues in quantum field theory and string theory Luis J. Boya; 7. Geometric aspects of the standard model and the mysteries of matter Florian Scheck; 8. Absence of singular continuous spectrum for some geometric Laplacians Leonardo A. Cano García; 9. Models for formal groupoids Iván Contreras; 10. Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity Andrés Vargas; 11. Regularized traces and the index formula for manifolds with boundary Alexander Cardona and César Del Corral; Index.

Alexander Cardona is Associate Professor in Mathematics, Universidad de los Andes, Bogotá, where he is part of the research group in geometry, topology and global analysis. His research interest includes a wide range of applications of mathematics in theoretical physics.
Iván Contreras is a PhD student at the Institute of Mathematics, University of Zurich, working in the mathematical physics group. His areas of interest cover the connection between geometry, topology and field theories.
Andrés F. Reyes-Lega is Associate Professor at the Physics Department, Universidad de los Andes, Bogotá, and is a member of the theoretical physics group. His recent research work has been in quantum field theory and quantum information theory.