On a covariant version of Caianiello's model

摘要

Caianiello's derivation of Quantum Geometry through an isometric embedding of the spacetime (M, (g) over tilde) in the pseudo-Riemannian structure (T*M, g* (AB) ) is reconsidered. In the new derivation, using a non-linear connection and the bundle formalism, we obtain a Lorentzian-type structure in the 4-dimensional manifold M that is covariant under arbitrary local coordinate transformations in M. We obtain that if models with maximal acceleration are non-trivial, gravity should be supplied with other interactions in a unification framework.