Representation theory in classical and quantum physics
(2006) Proc. Fourth Int. Workshop on Contemporary Problems in Mathematical Physics (Cotonou, Bénin, Nov. 2005) — ISBN: [9812568530], p. 3-64, published
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- Authors
Antoine, Jean-Pierre 
- Abstract
- We review the basic notions of group theory, in particular Lie groups and Lie algebras, and of representations of the latter. Then we examine briefly their occurrence in classical physics for the description of invariance properties of physical systems and the concomitant conservation laws resulting from Noether's theorem. In the last section, finally, we give an overview of the applications of group representation theory in quantum physics, with special emphasis on the proper mathematical description of symmetry properties, both in quantum mechanics and in quantum field theory.
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