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Quantum Fields and Strings: A Course for Mathematicians
Edited by: Pierre Deligne, Institute for Advanced Study, Princeton, NJ, Pavel Etingof, Massachusetts Institute of Technology, Cambridge, MA, Daniel S. Freed, University of Texas, Austin, TX, Lisa C. Jeffrey, University of Toronto, ON, Canada, David Kazhdan, Harvard University, Cambridge, MA, John W. Morgan, Columbia University, New York, NY, David R. Morrison, Duke University, Durham, NC, and Edward Witten, Institute for Advanced Study, Princeton, NJ

1999; 1501 pp; softcover
ISBN-10: 0-8218-2014-1
ISBN-13: 978-0-8218-2014-8
List Price: US$65
Member Price: US$52
Order Code: QFT/1/2.S
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Ideas from quantum field theory and string theory have had considerable impact on mathematics over the past 20 years. Advances in many different areas have been inspired by insights from physics.

In 1996-97 the Institute for Advanced Study (Princeton, NJ) organized a special year-long program designed to teach mathematicians the basic physical ideas which underlie the mathematical applications. The purpose is eloquently stated in a letter written by Robert MacPherson: "The goal is to create and convey an understanding, in terms congenial to mathematicians, of some fundamental notions of physics ... [and to] develop the sort of intuition common among physicists for those who are used to thought processes stemming from geometry and algebra."

These volumes are a written record of the program. They contain notes from several long and many short courses covering various aspects of quantum field theory and perturbative string theory. The courses were given by leading physicists and the notes were written either by the speakers or by mathematicians who participated in the program. The book also includes problems and solutions worked out by the editors and other leading participants. Interspersed are mathematical texts with background material and commentary on some topics covered in the lectures.

These two volumes present the first truly comprehensive introduction to this field aimed at a mathematics audience. They offer a unique opportunity for mathematicians and mathematical physicists to learn about the beautiful and difficult subjects of quantum field theory and string theory.


Graduate students and research mathematicians working in various areas of mathematics related to quantum field theory.


"An immense amount of valuable material on recent developments. The development of classical supersymmetry by Deligne and collaborators is careful and systematic ... masterful treatment ... the book is a magnificent achievement."

-- SIAM Review

"A concise introduction to the quantum field theory and perturbative string theory, with as much emphasis on a mathematically satisfying exposition and clarity as possible ... will be helpful to all mathematicians and mathematical physicists who wish to learn about the beautiful subject of quantum field theory."

-- European Mathematical Society Newsletter

Table of Contents

Volume 1, Part 1. Classical Fields and Supersymmetry
  • P. Deligne and J. W. Morgan -- Notes on supersymmetry (following Joseph Bernstein)
  • P. Deligne -- Notes on spinors
  • P. Deligne and D. S. Freed -- Classical field theory
  • P. Deligne and D. S. Freed -- Supersolutions
  • P. Deligne and D. S. Freed -- Sign manifesto
Volume 1, Part 2. Formal Aspects of QFT
  • P. Deligne -- Note on quantization
  • D. Kazhdan -- Introduction to QFT
  • E. Witten -- Perturbative quantum field theory
  • E. Witten -- Index of Dirac operators
  • L. Faddeev -- Elementary introduction to quantum field theory
  • D. Gross -- Renormalization groups
  • P. Etingof -- Note on dimensional regularization
  • E. Witten -- Homework
  • Index
Volume 2, Part 3. Conformal Field Theory and Strings
  • K. Gawędzki -- Lectures on conformal field theory
  • E. D'Hoker -- Perturbative string theory
  • P. Deligne -- Super space descriptions of super gravity
  • D. Gaitsgory -- Notes on 2d conformal field theory and string theory
  • A. Strominger -- Kaluza-Klein compactifications, supersymmetry, and Calabi-Yau spaces
Volume 2, Part 4. Dynamical Aspects of QFT
  • E. Witten -- Dynamics of Quantum Field Theory
  • N. Sieberg -- \(N = 1\) supersymmetric field theories in four dimensions
  • Index
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