Open Access
Translator Disclaimer
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

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.

Citation

Download Citation

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

Information

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

JOURNAL ARTICLE
67 PAGES


SHARE
Back to Top