The Hopf algebra of identical, fermionic particle systems—Fundamental concepts and properties

Abstract

The Hopf algebra structure of the fermionic Fock space is unravelled. The tools provided by the Hopf algebra formalism are used to rederive in a more straightforward fashion some known theorems and to open the way to natural generalizations of these results. The algebraic concepts of rank, depth and length of a wave function are given. They allow one to cast a wave function into a canonical form that is simpler and more appropriate to a physical interpretation or a numerical treatment. An original algorithm to re-expand a wave function with the least possible number of spin orbitals is described.