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Recursive Fermion System in Cuntz Algebra.I -- Embeddings of Fermion Algebra into Cuntz Algebra ---

Mitsuo Abe·Katsunori Kawamura
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Abstract

Embeddings of the CAR (canonical anticommutation relations) algebra of fermions into the Cuntz algebra ${\cal O}_2$ (or ${\cal O}_{2d}$ more generally) are presented by using recursive constructions. As a typical example, an embedding of CAR onto the U(1)-invariant subalgebra of ${\cal O}_2$ is constructed explicitly. Generalizing this construction to the case of ${\cal O}_{2^p}$, an embedding of CAR onto the U(1)-invariant subalgebra of ${\cal O}_{2^p}$ is obtained. Restricting a permutation representation of the Cuntz algebra, we obtain the Fock representation of CAR. We apply the results to embed the algebra of parafermions of order $p$ into ${\cal O}_{2^p}$ according to the Green's ansatz.

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Mitsuo Abe, Katsunori Kawamura. 2001-10-01. Recursive Fermion System in Cuntz Algebra.I -- Embeddings of Fermion Algebra into Cuntz Algebra ---. https://arxiv.org/abs/math-ph/0110003

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