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

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.(C) 2003 American Institute of Physics.