Quantum Fields and Strings

A Course for Mathematicians

Pierre Deligne

1502 pages, parution le 01/01/1999

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Résumé

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

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

Caractéristiques techniques

	PAPIER
Éditeur(s)	American Mathematical Society (AMS)
Auteur(s)	Pierre Deligne
Parution	01/01/1999
Nb. de pages	1502
Couverture	Broché
Intérieur	Noir et Blanc
EAN13	9780821820148
ISBN13	978-0-8218-2014-8