General boson expansion theory and Lie algebrasBnandDn

Abstract

A general boson expansion theory for even and odd fermion states has been developed in both Dyson and unitary representations. We can construct them in several different forms, one of which essentially reproduces the formula of Marshalek. The underlying algebra may or may not obey the associative law. A connection of the theory with the Lie algebras $B_n$ and $D_n$ has been investigated. As a byproduct, construction of fermion annihilation and creation operators solely in terms of boson operators has been found.