Recursive Fermion System in Cuntz Algebra. I
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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2002
 DOI:
 10.1007/s002200200651
 Bibcode:
 2002CMaPh.228...85A