Quantization of space-time and the corresponding quantum mechanics

An axiomatic framework for describing general space-time models is presented. Space-time models to which irreducible propositional systems belong as causal logics are quantum (q) theoretically interpretable and their event spaces are Hilbert spaces. Such aq space-time is proposed via a canonical quantization. As a basic assumption, the time t and the radial coordinate r of aq particle satisfy the canonical commutation relation t,r]=±i . The two cases will be considered simultaneously. In that case the event space is the Hilbert space L²(³). Unitary symmetries consist of Poincaré-like symmetries (translations, rotations, and inversion) and of gauge-like symmetries. Space inversion implies time inversion. Thisq space-time reveals a confinement phenomenon: Theq particle is confined in an size region of Minkowski space at any time. One particle mechanics overq space-time provides mass eigenvalue equations for elementary particles. Prugoveki's stochasticq mechanics andq space-time offer a natural way for introducing and interpreting consistently such aq space-time andq particles existing in it. The mass eigenstates ofq particles generate Prugoveki's extended elementary particles. When 0, these particles shrink to point particles and is recovered as the classical (c) limit ofq space-time. Conceptual considerations favor the case t,r]=+i , and applications in hadron physics give the fit 2/5 fermi/GeV.This paper is a revised version of the author's work, Quantization of Space-time and the Corresponding Quantum Mechanics (Part I), report KFKI-1981-48.