Loop groups

Andrew Pressley and Graeme Segal

Loop groups are the simplest class of infinite dimensional Lie groups, and have important applications in elementary particle physics. They have recently been studied intensively, and the theory is now well developed, involving ideas from several areas of mathematics - algebra, geometry, analysis, and combinatorics. The mathematics of quantum field theory is an important ingredient. This book gives a complete and self-contained account of what is known about the subject and it is written from a geometrical and analytical point of view, with quantum field theory very much in mind. The mathematics used in connection with loop groups is interesting and important beyond its immediate applications and the authors have tried to make the book accessible to mathematicians in many fields as well as researchers in pure mathematicians, theoretical physicists and graduate students.

「Nielsen BookData」より

This book is intended for research pure mathematicians and theoretical physicists and graduate students.

「Nielsen BookData」より


  • Introduction
  • PART 1 - Finite dimensional lie groups
  • Groups of smooth maps
  • Central extensions
  • The root system: KAC-Moody algebras
  • Loop groups as groups of operators in Hilbert space
  • The Grassmannian of Hilbert space and the determinant line bundle
  • The fundamental homogeneous space. PART 2 - Representation theory
  • The fundamental representation
  • The Borel-Weil theory
  • The spin representation
  • 'Blips' or 'vertex operators'
  • The KAC character formula and the Bernstein-Gelfand-Gelfand resolution
  • References
  • Index of notation
  • Index.

「Nielsen BookData」より


書名 Loop groups
著作者等 Pressley, Andrew
Segal, Graeme
シリーズ名 Oxford mathematical monographs
出版元 Clarendon Press
刊行年月 1986
版表示 New ed
ページ数 viii, 318 p.
大きさ 25 cm
ISBN 0198535619
NCID BA00259298
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言語 英語
出版国 イギリス