The representation theory of the Heisenberg group and beyond

In this paper we present some recent and new developments in the theory of p{ mechanics. p{Mechanics is a consistent physical theory which contains both classical and quantum mechanics. The Heisenberg group and its representation theory is the basis of p{mechanics. We give a summary of recent results on p{mechanical observables, states and canonical transformations. In doing so we exhibit relations between the quantum and classical image of these objects. We also present some new work on the Kepler/Coulomb problem. This involves constructing a new Hilbert space which represents the dynamics of the Kepler/Coulomb problem in a simple form