Abstract
Based on our previous work on the recursive fermion system in the Cuntz algebra, it is shown that a nonlinear transformation group of the CAR fermion algebra is induced from a U(2p) action on the Cuntz algebra \(\mathcal{O}\) 2 p with an arbitrary positive integer p. In general, these nonlinear transformations are expressed in terms of finite polynomials in generators. Some Bogoliubov transformations are involved as special cases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abe, M. and Kawamura, K.: Recursive fermion system in Cuntz algebra. I, Embeddings of fermion algebra into Cuntz algebra, to appear in Comm. Math. Phys. (2002), Preprint RIMS-1332, math-ph/0110003.
Abe, M. and Kawamura, K.: Recursive fermion system in Cuntz algebra. II, Endomorphism, automorphism and branching of representation, in preparation.
Cuntz, J.: Simple C*-algebras generated by isometries, Comm. Math. Phys. 57 (1977), 173–185.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Abe, M., Kawamura, K. Nonlinear Transformation Group of CAR Fermion Algebra. Letters in Mathematical Physics 60, 101–107 (2002). https://doi.org/10.1023/A:1016114322568
Issue Date:
DOI: https://doi.org/10.1023/A:1016114322568