Phase Space Description of Quantum Mechanics and Non-commutativity

Basil Hiley

In the second talk I would like to present some new work that I have been doing on phase space descriptions in general. I would like to show the connection between the Bohm approach and the Wigner-Moyal approach. I will then show how you can look at the Bohm theory in an extended Heisenberg picture giving a very different take on the quantum potential. In this approach the symplectic group and its covering group, the metaplectic group play a key role. Behind this group structure is the symplectic Clifford algebra an analogue of the well know orthogonal Clifford algebra. I hope to bring out some of the consequences of these mathematical structures including my suggestion for non-commutative geometries, but I won't go into the details in this forum.