Mathematical Foundations of Quantum Field Theory and Perturbative String Theory

Mathematical Foundations of Quantum Field Theory and Perturbative String Theory

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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 organised under three main chapters: Foundations for Quantum Field Theory, Quantisation 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.
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Product details

  • Hardback | 357 pages
  • 177.8 x 254 x 25.4mm | 793.79g
  • Providence, United States
  • English
  • 0821851950
  • 9780821851951
  • 2,495,701

Table of contents

Introduction by H. Sati and U. Schreiber Foundations for quantum field theory: Models for $(\infty,n)$-categories and the cobordism hypothesis by J. E. Bergner From operads to dendroidal sets by I. Weiss Field theories with defects and the centre functor by A. Davydov, L. Kong, and I. Runkel Quantization of field theories: Homotopical Poisson reduction of gauge theories by F. Paugam Orientifold precis by J. Distler, D. S. Freed, and G. W. Moore Two-dimensional quantum field theories: Surface operators in 3d topological field theory and 2d rational conformal field theory by A. Kapustin and N. Saulina Conformal field theory and a new geometry by L. Kong Collapsing conformal field theories, spaces with non-negative Ricci curvature and non-commutative geometry by Y. Soibelman Supersymmetric field theories and generalized cohomology by S. Stolz and P. Teichner Topological modular forms and conformal nets by C. L. Douglas and A. G. Henriques
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