Recursive Fermion System in Cuntz Algebra. I
Abstract
Embeddings of the CAR (canonical anticommutation relations) algebra of fermions into the Cuntz algebra ?2 (or ?2d 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 ?2p, an embedding of CAR onto the U(1)-invariant subalgebra of ?2p 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 ?2p according to Green's ansatz.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- 2002
- DOI:
- 10.1007/s002200200651
- Bibcode:
- 2002CMaPh.228...85A