On a covariant version of Caianiello’s model

Abstract

Caianiello's derivation of Quantum Geometry through an isometric embedding of the spacetime ({\bf M},\tilde{g}) in the pseudo-Riemannian structure ({\bf T^*M},g^*_{AB}) is reconsidered. In the new derivation, a non-linear connection and the bundle %%@ formalism induce a Lorentzian-type structure in the 4-dimensional manifold {\bf M} that is covariant %%@ under arbitrary local coordinate transformations in {\bf M}. If models with maximal acceleration are required to be non-trivial, gravity should be supplied with other interactions in a unification framework.