  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.
