**Proceedings of Symposia in Pure Mathematics**

Volume: 83;
2011;
354 pp;
Hardcover

MSC: Primary 81; 70; 18; 55;

Print ISBN: 978-0-8218-5195-1

Product Code: PSPUM/83

List Price: $100.00

AMS Member Price: $80.00

MAA member Price: $90.00

**Electronic ISBN: 978-0-8218-8334-1
Product Code: PSPUM/83.E**

List Price: $100.00

AMS Member Price: $80.00

MAA member Price: $90.00

# Mathematical Foundations of Quantum Field Theory and Perturbative String Theory

Share this page *Edited by *
*Hisham Sati; Urs Schreiber*

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.

#### Readership

Graduate students and research mathematicians interested in mathematical aspects of quantum field theory.

# Table of Contents

## Mathematical Foundations of Quantum Field Theory and Perturbative String Theory

- Contents v6 free
- Preface vii8 free
- Introduction 110 free
- Foundations for Quantum Field Theory 1524
- Quantization of Field Theories 129138
- Two-Dimensional Quantum Field Theories 173182
- Surface operators in 3d TFT and 2d rational CFT 175184
- Conformal field theory and a new geometry 199208
- Collapsing conformal field theories, spaces with non-negative Ricci curvature and non-commutative geometry 245254
- Supersymmetric field theories and generalized cohomology 279288
- Topological modular forms and conformal nets 341350