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Loop Groups : Oxford Mathematical Monographs - Andrew Pressley

Loop Groups

Oxford Mathematical Monographs

Paperback

Published: 9th June 1988
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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.

'This is an outstanding book, of enormous interest to anyone interested in Lie groups, Lie algebras and/or Quantum Field Theory' Mathematika

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.

ISBN: 9780198535614
ISBN-10: 0198535619
Series: Oxford Mathematical Monographs
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 328
Published: 9th June 1988
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 23.3 x 15.5  x 1.7
Weight (kg): 0.54