A generalisation of the process of normal quantisation is studied which deals with a physical system whose phase space is given by a coadjoint orbit of a locally compact Lie group G. Under certain conditions, an algebra structure—implemented by a Fronsdal *-product—is assigned to the family of physical observables in such a way that the normal quantisation provides a representation of the algebra. This method, then, provides a useful means of determining a physically sensible Fronsdal *-product for a given system.
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Keith C. Hannabuss, Mark A. Hennings, Some Aspects of Normal Quantisation. Publ. Res. Inst. Math. Sci. 21 (1985), no. 6, pp. 1337–1352DOI 10.2977/PRIMS/1195178520