Infinite-Dimensional Lie Groups and Algebras in Mathematical Physics

We give a review of infinite-dimensional Lie groups and algebras and show some applications and examples in mathematical physics. This includes diffeomorphism groups and their natural subgroups like volume-preserving and symplectic transformations, as well as gauge groups and loop groups. Applicatio...

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Bibliographic Details
Published inAdvances in Mathematical Physics Vol. 2010; no. 1; pp. 196 - 230
Main Author Schmid, Rudolf
Format Journal Article
LanguageEnglish
Published New York Hindawi Limiteds 01.01.2010
Hindawi Publishing Corporation
Hindawi Limited
Subjects
Algebra
Banach spaces
Computational fluid dynamics
Gravitation
Lie groups
Mathematical analysis
Mathematical problems
Maxwell's equations
Relativity
Subgroups
Symmetry
Transformations
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Summary:We give a review of infinite-dimensional Lie groups and algebras and show some applications and examples in mathematical physics. This includes diffeomorphism groups and their natural subgroups like volume-preserving and symplectic transformations, as well as gauge groups and loop groups. Applications include fluid dynamics, Maxwell's equations, and plasma physics. We discuss applications in quantum field theory and relativity (gravity) including BRST and supersymmetries.
Bibliography:ObjectType-Article-2
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ISSN:1687-9120
1687-9139
DOI:10.1155/2010/280362