Unitary isomorphism of Fock spaces of bosons and fermions arising from a representation of the Cuntz algebra 2

Abstract

Bosons and fermions are described by using canonical generators of Cuntz algebras on any permutative representation. According to branching laws associated with these descriptions, a certain representation of the Cuntz algebra 2 induces Fock representations HB and HF of bosons and fermions simultaneously. From this, a unitary operator U from HB to HF is obtained. We show the explicit formula of the action of U on the standard basis of HB. It is shown that U preserves the particle number of HB and HF.