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

Katsunori Kawamura

doi:10.1063/1.2988719

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arXiv · 0807.2702

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

Katsunori Kawamura

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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 ${\cal H}_{B}$ 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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BibTeX RIS

Katsunori Kawamura. 2008-07-17. Unitary isomorphism of Fock spaces of bosons and fermions arising from a representation of the Cuntz algebra $\co{2}$. https://doi.org/10.1063/1.2988719

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