Coherent states of the q-canonical commutation relations

authored by

P. E. T. Jo rgensen, R. F. Werner

Abstract

For the q-deformed canonical commutation relations a(f)a*(g)= (1 - q)[f, g] 1 + qa*(g)a(f) for f, g in some Hilbert space H we consider representations generated from a vector f)f, where phiin H. We show that such a representation exists if and only if normphi. Moreover, for normphi, these representations are unitarily equivalent to the Fock representation (obtained for ). On the other hand representations obtained for different unit vectors phi are disjoint. We show that the universal C*-algebra for the relations has a largest proper, closed, two-sided ideal. The quotient by this ideal is a natural q-analogue of the Cuntz algebra (obtained for q = 0). We discuss the conjecture that, for d lt this analogue should, in fact, be equal to the Cuntz algebra itself. In the limiting cases q = we determine all irreducible representations of the relations, and characterize those which can be obtained via coherent states.

Organisation(s)

Institute of Theoretical Physics

Type

Article

Journal

Comm. Math. Phys.

Volume

164

Pages

455-471

No. of pages

17

Publication date

1994

Publication status

Published

Peer reviewed

Yes

Electronic version(s)

https://doi.org/10.1007/BF02101486 (Access: Unknown)