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2004 Infinite Dimentional Lie Groups with Applications to Mathematical Physics
Rudolf Schmid
J. Geom. Symmetry Phys. 1: 54-120 (2004). DOI: 10.7546/jgsp-1-2004-54-120


We give a survey of infinite dimensional Lie groups and show some applications and examples in mathematical physics. This includes diffeomorphism groups and their natural subgroups like volume preserving, symplectic and contact transformations, as well as gauge groups, quantomorphisms and loop groups. Various applications include fluid dynamics, Maxwell’s equations, plasma physics and BRST symmetries in quantum field theory. We discuss the Lie group structures of pseudodifferential and Fourier integral operators, both on compact and non- compact manifolds and give applications to the KdV equation and quantization.


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Rudolf Schmid. "Infinite Dimentional Lie Groups with Applications to Mathematical Physics." J. Geom. Symmetry Phys. 1 54 - 120, 2004.


Published: 2004
First available in Project Euclid: 23 May 2017

zbMATH: 1063.22020
MathSciNet: MR2096565
Digital Object Identifier: 10.7546/jgsp-1-2004-54-120

Rights: Copyright © 2004 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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