Formulation of noncommutative quantum mechanics in terms of Hilbert-Schmidt operators

Noncommutative quantum mechanics can be considered as a quantum system represented in the space of Hilbert-Schmidt operators acting on noncommutative configuration space. We review the recent advances in this field, including the Moyal and Voros product formulation, quantum wave equation and potentials, scattering theory, path integrals, statistical and thermodynamical properties of a noncommutative gas.