Frame quantization and finite quantum systems

Abstract

This work gives examples of star-products on discrete systems. The star-product arises from frame quantization, in the spirit of the Berezin-Toeplitz or anti-Wick quantization. Frames are the discrete versions of coherent states and thus, naturally associated to such frame quantizations are various quasiprobability distributions, which are necessary in the phase space representations of quantum mechanics. In the construction using the irreducible unitary representations for dihedral groups, we have shown the important objects in the phase space quantum mechanics.