Remarks on a Relation between BZ Boson Expansion and Algebraic Recursion Formulas Constructed in so(2n)

Abstract

In the previous paper (referred to as (I)), 1l we introduced the recursion formulas defined in terms of the pair operators which span the algebra so (2n) (n; dimension number of a system). We pointed out that there exists an interesting problem on a relation between the EZ boson expansion and our recursion formulas. Marshalek and Holzwarth proved the following: The pair operators satisfy the relations of the density matrix K in the Hartree-Eogoliubov (HE) theory (K =K2) under the c-number replacement of the bosons in the EZ expansion. From this proof, they concluded that the EZ expansion method may be regarded as an a priori quantized time-dependent HE theory. 2t However, in their c-number treatment, quantized relations of K=K2 could not be obtained. In this note, we will prove that Eqs. (I-3. 11) and (I-3. 12) can be regarded as the quantized relations of K=K2• First, we define ideal boson operators: