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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.
Table of Contents
A brief introduction to Dirac manifolds
Differential geometry of holomorphic vector bundles on a curve
Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles
Introduction to Feynman integrals
Iterated integrals in quantum field theory
Geometric issues in quantum field theory and string theory
Geometric aspects of the standard model and the mysteries of matter
Absence of singular continuous spectrum for some geometric Laplacians
Models for formal groupoids
Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity
Regularized traces and the index formula for manifolds with boundary
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