On a covariant version of Caianiello's Model

TL;DR

This paper revisits Caianiello's Quantum Geometry model, introducing a covariant approach using non-linear connections that maintains Lorentzian structure under coordinate transformations, and discusses implications for unification with other interactions.

Contribution

It presents a covariant formulation of Caianiello's model using bundle formalism and non-linear connections, enhancing the geometric consistency of quantum gravity models.

Findings

The model achieves covariance under arbitrary coordinate transformations.

A Lorentzian structure is induced in the spacetime manifold.

Implications for unification with other fundamental interactions are discussed.

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.