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Mathematical Foundations of Quantum Field Theory and Perturbative String Theory

Edited by: Hisham Sati University of Pittsburgh, Pittsburgh, PA
Urs Schreiber Utrecht University, Utrecht, The Netherlands
Available Formats:
Hardcover ISBN: 978-0-8218-5195-1
Product Code: PSPUM/83
List Price: $106.00 MAA Member Price:$95.40
AMS Member Price: $84.80 Electronic ISBN: 978-0-8218-8334-1 Product Code: PSPUM/83.E List Price:$100.00
MAA Member Price: $90.00 AMS Member Price:$80.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $159.00 MAA Member Price:$143.10
AMS Member Price: $127.20 Click above image for expanded view Mathematical Foundations of Quantum Field Theory and Perturbative String Theory Edited by: Hisham Sati University of Pittsburgh, Pittsburgh, PA Urs Schreiber Utrecht University, Utrecht, The Netherlands Available Formats:  Hardcover ISBN: 978-0-8218-5195-1 Product Code: PSPUM/83  List Price:$106.00 MAA Member Price: $95.40 AMS Member Price:$84.80
 Electronic ISBN: 978-0-8218-8334-1 Product Code: PSPUM/83.E
 List Price: $100.00 MAA Member Price:$90.00 AMS Member Price: $80.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$159.00 MAA Member Price: $143.10 AMS Member Price:$127.20
• Book Details

Proceedings of Symposia in Pure Mathematics
Volume: 832011; 354 pp
MSC: Primary 81; 70; 18; 55;

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

• 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 ]
• Additional Material

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 832011; 354 pp
MSC: Primary 81; 70; 18; 55;

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.

• 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 ]
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.