Semisimple Subalgebras of Semisimple Lie Algebras: The Algebra (SU(6)) as a Physically Significant Example

Abstract

Lie algebras and their representations enter physics in many ways. They have wide applicability such as in the various shell models that are used in physics, the atomic shell model, the nuclear shell model, and the molecular shell model. In these shell models and in other applications of Lie algebra theory in physics, the specified subsets of states of a physical system are found to transform like irreducible representations of semisimple Lie algebras, G, of rank greater than 1. The algebras G might have no immediate physical significance. This chapter discusses Dynkin's theory for the embedding of semisimple complex Lie algebras in semisimple complex Lie algebras, in view of the wide area of applicability of this theory to the problems of physics. The group SU(6) and chains of subgroups of SU(6) are used in the shell model of atomic physics.