Phase Space Description of Quantum Mechanics and Non-commutative Geometry: Wigner-Moyal and Bohm in a wider context

In this paper we approach the question of the existence of a x, p phase space in a new way. Rather than abandoning all hope of constructing such a phase-space for quantum phenomena, we take aspects from both the Wigner-Moyal and Bohm approaches and show that although there is no unique phase space we can form ‘shadow’ phase spaces. We then argue that this is a consequence of the noncommutative geometry defined by the operator algebra.