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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, 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.
Contents
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.
