A Deformation of Quantum Dynamics through the Phase Space Path Integral

Using a regularised construction of the phase space path integral due to Ingrid Daubechies and John Klauder which involves a time scale ultimately taken to vanish, and motivated by the general programme towards a noncommutative space(time) geometry, physical consequences of assuming this time parameter to provide rather a new fundamental time scale are explored in the context of the one dimensional harmonic oscillator. Some tantalising results are achieved, which raise intriguing prospects when extrapolated to the quantum field theory and gravitational contexts.