Quantum fields and strings : a course for mathematicians

著者

書誌事項

Quantum fields and strings : a course for mathematicians

Pierre Deligne ... [et al.], editors

American Mathematical Society, c1999

  • : set
  • v. 1
  • v. 2

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注記

Written record of a special year-long program organized by the Institute for Advanced Study (Princeton, NJ) in 1996-97

Includes bibliographical references and index

内容説明・目次

巻冊次

: set ISBN 9780821811986

内容説明

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, New Jersey) organized a special year-long programme designed to teach mathematicians the basic physical ideas which underlie the mathematical applications. The purpose was to create and convey an understanding, in terms useful to mathematicians, of some fundamental notions of physics and 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 programme. 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 programme. The book also includes problems and solutions worked out by the editors and participants. Interspersed are mathematical texts with background material and commentary on some topics covered in the lectures.

目次

  • Volume 1 - Part 1 Classical fields and supersymmetry: notes on supersymmetry
  • notes on spinors
  • classical field theory
  • supersolutions
  • sign manifesto. Volume 1 - Part 2 Formal aspects of QFT: note on quantization
  • introduction to QFT
  • perturbative quantum field theory
  • index of Dirac operators
  • elementary introduction to quantum field theory
  • renormalization groups
  • note on dimensional regularization
  • homework. Volume 2 - Part 3 Conformal field theory and strings: lectures on conformal field theory
  • perturbative string theory
  • super space descriptions of super gravity
  • notes on 2d donformal field theory and string theory
  • Kaluza-Klein compactifications, supersymmetry and Calabi-Yau spaces. Volume 2 - Part 4 Dynamical aspects of QFT: dynamics of quantum field theory
  • $N = 1$ supersymmetric field theories in four dimensions.
巻冊次

v. 1 ISBN 9780821820124

内容説明

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.
巻冊次

v. 2 ISBN 9780821820131

内容説明

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.

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