DEFORMATION OF THE QUANTUM-MECHANICAL PHASE-SPACE WITH BOSONIC OR FERMIONIC COORDINATES

We describe the one-parameter deformation of the phase space of a quantum mechanical system and show that this twisted phase space is covariant under the action of the symplectic quantum group. The analogous case of a system with fermionic coordinates is also considered and the phase space is shown to be covariant under the action of the orthogonal quantum group. Twisted commutation relations occur in the description of deformed spaces or superspaces as well as in the formulation of field theories with generalized statistics. The many-parameter case is briefly discussed.