Abstract
It is shown for a family of *-products (i.e. different ordering rules) that, under a strong invariance condition, the functions of the quadratic preferred observables (which generate the Cartan subalgebra in phase space realization of Lie algebras) take only the linear or exponential form. An exception occurs for the case of a symmetric ordering *-product where trigonometric functions and two special polynomials can also be included. As an example, the ‘quantized algebra’ of the oscillator Lie algebra is argued.
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References
Drinfel'd, V., Quantum Groups, in Proc. of ICM Berkeley 1986, I798. Jimbo, M., Lett. Math. Phys. 10, 63 (1985).
Biedenharn, L. C., J. Phys. A 22, L878 (1989); Sun, C. P. and Fu, H. C., J. Phys. A 22, L983 (1989); Macfarlane, A. J., J. Phys. A 22, 4581 (1989).
FlatoM. and LuZ. C., Lett. Math. Phys. 21, 85 (1991) (see also [8]).
FlatoM. and SternheimerD., Lett. Math. Phys. 22, 155 (1991).
BayenF., FlatoM., FronsdalC., LichnerowiczA., and SternheimerD., Ann. Phys. (N.Y.) 111, 61–111 (1978)
VeyJ., Comment. Math. Helv. 50, 421 (1975).
ArgawalG. S. and WolfE., Phys. Rev. D 2, 2161 (1968).
LuZ. C., J. Math. Phys. 33, 446 (1992).
ArnalD., CortetJ. C., MolinP., and PinczonG., J. Math. Phys. 22, 276 (1983).
Flato, M., Lu, Z. C., and Sternheimer, D., to appear in Foundations of Physics (Barut issue).
SternheimerD., AMS Lectures in Applied Mathematics vol. 21, 255 (1985).
ConnesA., FlatoM., and SternheimerD., Lett. Math. Phys. 24, 1 (1992).