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.

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.