Permutation Groups and Many-Electron States

Abstract

In this chapter we discuss the properties of permutation groups, which are known as “Symmetric Groups” in the mathematics literature. Although permutation groups are quite generally applicable to many-body systems, they are used in this chapter to classify the symmetry in many-electron states. This discussion applies to the symmetries of both the spin and orbital states. In Chap. 18 we apply the results of this chapter for the permutation groups to show a very different use of permutation groups, which is to classify the symmetry properties for tensors occuring in solid state physics in a powerful way.