Journal of Geometry and Symmetry in Physics

Infinite Dimentional Lie Groups with Applications to Mathematical Physics

Rudolf Schmid

Full-text: Open access

Abstract

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.

Article information

Source
J. Geom. Symmetry Phys., Volume 1 (2004), 54-120.

Dates
First available in Project Euclid: 23 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.jgsp/1495505067

Digital Object Identifier
doi:10.7546/jgsp-1-2004-54-120

Mathematical Reviews number (MathSciNet)
MR2096565

Zentralblatt MATH identifier
1063.22020

Citation

Schmid, Rudolf. Infinite Dimentional Lie Groups with Applications to Mathematical Physics. J. Geom. Symmetry Phys. 1 (2004), 54--120. doi:10.7546/jgsp-1-2004-54-120. https://projecteuclid.org/euclid.jgsp/1495505067


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