Geometric, Algebraic and Topological Methods for Quantum Field Theory

Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory.

This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists.

Contents:

• Lectures:

  • Spectral Geometry (B Iochum)
  • Index Theory for Non-compact G-manifolds (M Braverman and L Cano)
  • Generalized Euler Characteristics, Graph Hypersurfaces, and Feynman Periods (P Aluffi)
  • Gravitation Theory and Chern-Simons Forms (J Zanelli)
  • Noncommutative Geometry Models for Particle Physics (M Marcolli)
  • Noncommutative Spacetimes and Quantum Physics (A P Balachandran)
  • Integrability and the AdS/CFT Correspondence (M Staudacher)
  • Compactifications of String Theory and Generalized Geometry (M Graña and H Triendl)

• Short Communications:

  • Groupoids and Poisson Sigma Models with Boundary (A Cattaneo and I Contreras)
  • A Survey on Orbifold String Topology (A Angel)
  • Grothendieck Ring Class of Banana and Flower Graphs (P Morales-Almazán)
  • On the Geometry Underlying a Real Lie Algebra Representation (R Vargas Le-Bert)

Readership: Researchers in geometry and topology, mathematical physics.
Key Features:

• Unique style aimed at a mixed readership of mathematicians and physicists
• Ideal for self-study or use in advanced courses or seminars