Recursive Fermion System in Cuntz Algebra. I |
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Authors: | Mitsuo Abe Katsunori Kawamura |
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Institution: | Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan.?e-mail: abe@kurims.kyoto-u.ac.jp; kawamura@kurims.kyoto-u.ac.jp, JP
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Abstract: | Embeddings of the CAR (canonical anticommutation relations) algebra of fermions into the Cuntz algebra ?2 (or ?2
d
more generally) are presented by using recursive constructions. As a typical example, an embedding of CAR onto the U(1)-invariant subalgebra of ?2 is constructed explicitly. Generalizing this construction to the case of ?2
p
, an embedding of CAR onto the U(1)-invariant subalgebra of ?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 ?2
p
according to Green's ansatz.
Received: 3 September 2001 / Accepted: 19 January 2002 |
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Keywords: | |
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