A covariant Quantum Geometry Model

Caianiello's fundamental derivation of Quantum Geometry through an isometric immersion procedure is reconsidered. In the new derivation, the non-linear connection and the bundle formalism induces a metric in the 4-dimensional space-time manifold ${\bf M}$ that is covariant under arbitrary local coordinate transformations of ${\bf M}$. These models have the intrinsic feature that gravity should be supplied with other interactions, if a consistent scheme with maximal acceleration is required. We argue that this fact can be understood in the general contest of Deterministic Finslerian Models