Quantum discrete phase space dynamics and its continuous limit

The main aspects of a discrete phase space formalism are presented and the discrete dynamical bracket, suitable for the description of time evolution in finite-dimensional spaces, is discussed. A set of operator bases is defined in such a way that the Weyl-Wigner formalism is shown to be obtained as a limiting case. In the same form, the Moyal bracket is shown to be the limiting case of the discrete dynamical bracket. The dynamics in quantum discrete phase spaces is shown not to be attained from discretization of the continuous case.