TY -的A2 -戈尔丁,g . a . AU -施密德,鲁道夫·PY - 2010 DA - 2010/08/23 TI - Infinite-Dimensional Lie Groups and Algebras in Mathematical Physics SP - 280362 VL - 2010 AB - 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. SN - 1687-9120 UR - https://doi.org/10.1155/2010/280362 DO - 10.1155/2010/280362 JF - Advances in Mathematical Physics PB - Hindawi Publishing Corporation KW - ER -