Dynamical origin of the $\star_\theta$-noncommutativity in field theory   from quantum mechanics
  We show that introducing an extended Heisenberg algebra in the context of the Weyl-Wigner-Groenewold-Moyal formalism leads to a deformed product of the classical dynamical variables that is inherited to the level of quantum field theory, and that allows us to relate the operator space noncommutativity in quantum mechanics to the quantum group inspired algebra deformation noncommutativity in field theory. 
Marcos Rosenbaum, J. David Vergara and L. Rom\'an Ju\'arez