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基本説明
In 1996-97 the Institute for Advanced Study (Princeton, NJ) organized a special year-long program designed to teach mathematicians the basic physical ideas. These volumes are a written record of the program.
Full Description
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.
Contents
Volume 1, Part 1. Classical Fields and Supersymmetry: Notes on supersymmetry (following Joseph Bernstein) by P. Deligne and J. W. Morgan Notes on spinors by P. Deligne Classical field theory by P. Deligne and D. S. Freed Supersolutions by P. Deligne and D. S. Freed Sign manifesto by P. Deligne and D. S. Freed Volume 1, Part 2. Formal Aspects of QFT: Note on quantization by P. Deligne Introduction to QFT by D. Kazhdan Perturbative quantum field theory by E. Witten Index of Dirac operators by E. Witten Elementary introduction to quantum field theory by L. Faddeev Renormalization groups by D. Gross Note on dimensional regularization by P. Etingof Homework by E. Witten Index Volume 2, Part 3. Conformal Field Theory and Strings: Lectures on conformal field theory by K. Gawedzki Perturbative string theory by E. D'Hoker Super space descriptions of super gravity by P. Deligne Notes on 2d conformal field theory and string theory by D. Gaitsgory Kaluza-Klein compactifications, supersymmetry, and Calabi-Yau spaces by A. Strominger Volume 2, Part 4. Dynamical Aspects of QFT: Dynamics of Quantum Field Theory by E. Witten $N = 1$ supersymmetric field theories in four dimensions by N. Sieberg Index.
