Noncommutative Distributions: Unitary Representation of Gauge Groups and Algebras

by Albeverio; Sergio

• ISBN13: 9780824791315
• ISBN10: 0824791312
• Format: Hardcover
• Copyright: 1993-08-26
• Publisher: CRC Press

Summary

Covering important aspects of the theory of unitary representations of nuclear Lie groups, this self-contained reference presents the general theory of energy representations and addresses various extensions of path groups and algebras.;Requiring only a general knowledge of the theory of unitary representations, topological groups and elementary stochastic analysis, Noncommutative Distributions: examines a theory of noncommutative distributions as irreducible unitary representations of groups of mappings from a manifold into a Lie group, with applications to gauge-field theories; describes the energy representation when the target Lie group G is compact; discusses representations of G-valued jet bundles when G is not necessarily compact; and supplies a synthesis of deep results on quasi-simple Lie algebras.;Providing over 200 bibliographic citations, drawings, tables, and equations, Noncommutative Distributions is intended for research mathematicians and theoretical and mathematical physicists studying current algebras, the representation theory of Lie groups, and quantum field theory, and graduate students in these disciplines.

Table of Contents

Basic functional groups and Lie algebras

Multiplicative G-distributions on a Riemannian manifold

The energy representations of gauge groups

Energy representation of path groups

The algebraic level - representations of current algebras

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