We consider questions related to the following quantization scheme: a classical variable f: Ω → ℝ on a phase space Ω is associated with a unique semispectral measure E f, such that the kth moment operator of E f is required to coincide with the operator integral L(f k, E) of f k with respect to a certain fixed phase space semispectral measure E. Mainly, we take the phase space Ω to be a locally compact unimodular group. In the concrete case where Ω = ℝ2 and E is a translation covariant semispectral measure, we determine explicitly the relevant operators L(f k, E) for certain variables f. In addition, we consider the question under what conditions a positive operator measure is projection valued.
|Number of pages
|Optics and Spectroscopy (English translation of Optika i Spektroskopiya)
|Published - 01 Sept 2007