In this paper we introduce a modified covariant quantum algebra based in the
so-called Quesne-Tkachuk algebra. By means of a deformation procedure we arrive
at a class of higher derivative models of gravity. The study of the particle
spectra of these models reveals an equivalence with the physical content of the
well-known renormalizable and super-renormalizable higher derivative gravities.
The particle spectrum exhibits the presence of spurious complex ghosts and, in
light of this problem, we suggest an interesting interpretation in the context
of minimal length theories. Also, a discussion regarding the non-relativistic
potential energy is proposed.Comment: Small corrections were made; improved figures; results unchanged;
published versio
