Recursive Fermion System in Cuntz Algebra.I  Embeddings of Fermion Algebra into Cuntz Algebra 
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.
 Publication:

arXiv eprints
 Pub Date:
 October 2001
 arXiv:
 arXiv:mathph/0110003
 Bibcode:
 2001math.ph..10003A
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Mathematical Physics;
 Mathematics  Operator Algebras;
 81R15 (Primary) 46L60 (Secondary)
 EPrint:
 14 pages, LaTeX