On interaction in extended particle model on (M4 x M4) x Z4

TL;DR

This paper formulates a comprehensive extended particle model on a four-sheeted space-time structure, incorporating local modes, symmetries, and state transitions, with detailed curvature and propagator calculations.

Contribution

It introduces a novel (M4 x M4) x Z4 model capturing interactions and state transitions of extended particles with detailed geometric and symmetry analysis.

Findings

Curvatures and propagators are explicitly determined.

Transitions between observable, unobservable, and partially observable states are modeled.

The model generalizes previous particle descriptions to a multi-sheeted space-time framework.

Abstract

A (M4 x M4) x Z4 model, describing an extended particle composed of two local modes and represented by a field psi(x, xi ;z), is formulated in its most general form (x, xi ; z) belong to (M4 x M4) x Z4. The 'z' argument specifies whether the particle is observable, unobservable, or partially observable (the latter case appears in two forms). In this four-sheeted structure, each sheet posses its own symmetry localized with respect to both space-times M4 inducing thereby connections in the continuous directions. Connections in the discrete direction describe transitions between observable, unobservable, and partially observable states. Curvatures and propagators are determined.