Details
| Original language | English |
|---|---|
| Pages (from-to) | 455-471 |
| Number of pages | 17 |
| Journal | Comm. Math. Phys. |
| Volume | 164 |
| Issue number | 3 |
| Publication status | Published - 1994 |
Abstract
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In: Comm. Math. Phys., Vol. 164, No. 3, 1994, p. 455-471.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Coherent states of the q-canonical commutation relations
AU - Jo rgensen, P. E. T.
AU - Werner, R. F.
PY - 1994
Y1 - 1994
N2 - 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.
AB - 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.
U2 - 10.1007/BF02101486
DO - 10.1007/BF02101486
M3 - Article
VL - 164
SP - 455
EP - 471
JO - Comm. Math. Phys.
JF - Comm. Math. Phys.
SN - 1432-0916
IS - 3
ER -