Infinite-Dimensional Lie Groups and Algebras in Mathematical Physics | Zendy

Rudolf Schmid | Zendy

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Infinite-Dimensional Lie Groups and Algebras in Mathematical Physics

Author(s) -

Rudolf Schmid

Publication year - 2010

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2010/280362

Subject(s) - diffeomorphism , symplectic geometry , brst quantization , physics , lie group , lie theory , gauge theory , lie algebra , gauge (firearms) , pure mathematics , mathematical physics , group (periodic table) , theoretical physics , mathematics , lie conformal algebra , quantum mechanics , adjoint representation of a lie algebra , archaeology , history

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

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