A coordinate independent formulation of the Weyl–Wigner transform theory.

Abstract

We present the Weyl–Wigner (WW) transform theory in a much more compact way than usual, by introducing the _ basis in an intrinsic form. This permits the derivation of new identities and also leads to generalizations, like the inclusion of /nite-dimensional systems in the WW theory, which is also discussed. We show, in this case, some striking di1erences in the structure of /nite phase space depending on the underlying dimension of quantum space being an even or odd integer.