Unitary isomorphism of Fock spaces of bosons and fermions arising from a representation of the Cuntz algebra $\co{2}$

Details Unitary isomorphism of Fock spaces of bosons and fermions arising from a representation of the Cuntz algebra $\co{2}$ Unitary isomorphism of Fock spaces of bosons and fermions arising from a representation of the Cuntz algebra $\co{2}$

2008-07-17

arxiv.org/abs/0807.2702v1

Mathematics

Operator Algebras

22 pages

Scientific paper

10.1063/1.2988719

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 $\co{2}$ induces Fock representations ${\cal H}_{B}$ and ${\cal H}_{F}$ of bosons and fermions simultaneously. From this, a unitary operator $U$ from ${\cal H}_{B}$ to ${\cal H}_{F}$ is obtained. We show the explicit formula of the action of $U$ on the standard basis of ${\cal H}_{B}$. It is shown that $U$ preserves the particle number of ${\cal H}_{B}$ and ${\cal H}_{F}$.

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