Phase space quantum mechanics via frame quantization on finite groups
In this work, the version of Wigner transforms and Wigner functions on discrete systems are formulated. Using frame quantization, the star-product of phase space functions are also computed for a particular finite group. Specifically, the Wigner transform, Wigner function and star-product are computed for the dicyclic group Dien. Frames are the discrete version of coherent states. In the literature, quasiprobability distributions are essential in the study of the phase space representations of quantum mechanics, and are naturally associated to frame quantizations. For this work, the unitary irreducible representations of a finite group play an essential role in the construction.
Delloro, F.D., & Nable, J.A. (2022). Phase space quantum mechanics via frame quantization on finite groups. AIP Conference Proceedings, 2472. https://doi.org/10.1063/5.0092639