ABSTRACT
Lie groups and algebras are used to describe continuous global and gauge symmetries in classical and quantum mechanics and in field theory. A familiar example is the description of rotational invariance in quantum mechanics. In particle physics Lie groups are useful not only for space-time symmetries such as translations, rotations, and Lorentz transformations, but also for internal symmetries such as isospin. It is assumed that the reader is familiar with such basic notions as irreducible representations (IRREPs), direct products, and irreducible tensor operators. Excellent introductions more detailed than the treatment here include (Georgi, 1999; Yndurain, 2007; Gilmore, 2005; Ramond, 2010; Barnes, 2010). Finite discrete groups are treated in detail in (Ramond, 2010), and more briefly in Sections 2.10 and 3.2.5.
