On the group of the independent-particle hamiltonian operator

Abstract

The detailed group structure of the independent-particle hamiltonian is derived in terms of interior and exterior products of groups describing various types of symmetry operations which commute with the hamiltonian. Modifications of this group due to external fields are examined, as are the concepts of the equivalence of particles. Simplifications due to isomorphisms and homomorphisms are outlined. Applications involving representations within this construction are examined.