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

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

22 pages

References in corpus (3)

• Generalized permutative representations of Cuntz algebras
• Recursive Fermion System in Cuntz Algebra. II -- Endomorphism, Automorphism and Branching of Representation --
• Recursive boson system in the Cuntz algebra ${\mathcal{O}}_{\infty }$

Cited by in corpus (2)

• Universal fermionization of bosons on permutative representations of the Cuntz algebra ${\mathcal{O}}_2$
• Jump transformations and an embedding of ${\mathcal{O}}_{\infty }$ into ${\mathcal{O}}_2$