Mathematical Foundations of Quantum Field Theory and Perturbative String Theory
About this Title
Hisham Sati, University of Pittsburgh, Pittsburgh, PA and Urs Schreiber, Utrecht University, Utrecht, The Netherlands, Editors
Publication: Proceedings of Symposia in Pure Mathematics
Publication Year 2011: Volume 83
ISBNs: 978-0-8218-5195-1 (print); 978-0-8218-8334-1 (online)
Conceptual progress in fundamental theoretical physics is linked with the search for the suitable mathematical structures that model the physical systems. Quantum field theory (QFT) has proven to be a rich source of ideas for mathematics for a long time. However, fundamental questions such as “What is a QFT?” did not have satisfactory mathematical answers, especially on spaces with arbitrary topology, fundamental for the formulation of perturbative string theory.
This book contains a collection of papers highlighting the mathematical foundations of QFT and its relevance to perturbative string theory as well as the deep techniques that have been emerging in the last few years.
The papers are organized under three main chapters: Foundations for Quantum Field Theory, Quantization of Field Theories, and Two-Dimensional Quantum Field Theories. An introduction, written by the editors, provides an overview of the main underlying themes that bind together the papers in the volume.
Graduate students and research mathematicians interested in mathematical aspects of quantum field theory.
Table of Contents
Foundations for quantum field theory
- Julia E. Bergner – Models for $(\infty , n)$-categories and the cobordism hypothesis [MR 2742424]
- Ittay Weiss – From operads to dendroidal sets [MR 2742425]
- Alexei Davydov, Liang Kong and Ingo Runkel – Field theories with defects and the centre functor [MR 2742426]
Quanitization of field theories
- Frédéric Paugam – Homotopical Poisson reduction of gauge theories [MR 2742427]
- Jacques Distler, Daniel S. Freed and Gregory W. Moore – Orientifold précis [MR 2742428]
Two-dimensional quantum field theories
- Anton Kapustin and Natalia Saulina – Surface operators in 3d topological field theory and 2d rational conformal field theory [MR 2742429]
- Liang Kong – Conformal field theory and a new geometry [MR 2742430]
- Yan Soibelman – Collapsing conformal field theories, spaces with non-negative Ricci curvature and non-commutative geometry [MR 2742431]
- Stephan Stolz and Peter Teichner – Supersymmetric field theories and generalized cohomology [MR 2742432]
- Christopher L. Douglas and André G. Henriques – Topological modular forms and conformal nets [MR 2742433]