Path integral action of a particle in the non commutative plane

Understand

Non commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non commutative configuration space.

• Taking this as departure point, we formulate a coherent state approach to the path integral representation of the transition amplitude.
• From this we derive an action for a particle moving in the non commutative plane and in the presence of an arbitrary potential.
• We find that this action is non local in time.