Coherent states of the q-canonical commutation relations

verfasst von

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.

Organisationseinheit(en)

Institut für Theoretische Physik

Typ

Artikel

Journal

Comm. Math. Phys.

Band

164

Seiten

455-471

Anzahl der Seiten

17

Publikationsdatum

1994

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

Elektronische Version(en)

https://doi.org/10.1007/BF02101486 (Zugang: Unbekannt)