Time evolving theory of the mechanics of single particles and single photons

Abstract

We introduce space-time ensemble methods to formulate definitions of single particles and single photons as local abstractions of constant processes. We find the general form of the corresponding Stueckelberg Lagrangian for Riemannian and Newtonian spacetimes and supply a physical interpretation for the worldline parameter. We develop the corresponding mechanical theories over the extended configuration space and the extended phase space. We suppose that the background can be represented by an ‘external field’ and we study several general examples. Certain phenomenological forms do not describe particles, others do not seem to describe theories in which the representation of the background is process independent (Riemannian case). At the canonical level the elimination of second-class constraints associated with null processes generates restrictions on the domain of definition of photon coordinates which correspond to the absence of zero energies. The requirement that the canonical process-anti-process classification exist leads to a factorization condition on the extended phase space which is satisfied for all the cases studied in which the configuration formalisms entail no difficulties, except one, which is the ‘minimally’ coupled external vector field case over Riemannian space-times. We discuss the observation theoretical significance of our results.