Finite Quantum Dynamics

Abstract

We general-quantize the dynamics of the quantum harmonic oscillator to obtain a covariant finite quantum dynamics in a finite quantum time. The usual central (``superselected'') time results from a self-organization. Unitarity necessarily fails, imperceptibly for middle times and grossly near the beginning and end of time. Time and energy interconvert during space-time decondensation or melt-down, at a rate governed by a constant like the Planck power.