Quantum twistors
  We compute explicitly a star product on the Minkowski space whose Poisson bracket is quadratic. This star product corresponds to a deformation of the conformal spacetime, whose big cell is the Minkowski spacetime. The description of Minkowski space is made in the twistor formalism and the quantization follows by substituting the classical conformal group by a quantum group. 
D. Cervantes, R. Fioresi, M. A. Lled\'o, F. A. Nadal
hep-th math.QA