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Book DetailsProceedings of Symposia in Pure MathematicsVolume: 83; 2011; 354 ppMSC: 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 TwoDimensional 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.ReadershipGraduate 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 ]

Twodimensional 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 nonnegative Ricci curvature and noncommutative 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 ]


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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 TwoDimensional 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.

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 ]

Twodimensional 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 nonnegative Ricci curvature and noncommutative 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 ]