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Advances in High Energy Physics
Volume 2017, Article ID 4768341, 8 pages
Research Article

Effective Models of Quantum Gravity Induced by Planck Scale Modifications in the Covariant Quantum Algebra

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Dr. Xavier Sigaud 150, Urca, 22290-180 Rio de Janeiro, RJ, Brazil
2Instituto Federal do Espírito Santo (IFES), Av. Vitória 1729, Jucutuquara, 29040-780 Vitória, ES, Brazil
3Departamento de Matemática, Física e Computação, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Rodovia Presidente Dutra, Km 298, Polo Industrial, 27537-000 Resende, RJ, Brazil

Correspondence should be addressed to G. P. de Brito; moc.liamg@inizzapovatsug

Received 26 May 2017; Accepted 13 August 2017; Published 26 September 2017

Academic Editor: Angel Ballesteros

Copyright © 2017 G. P. de Brito et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


We introduce modified covariant quantum algebra based on 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 equivalence with the physical content of the well-known 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 nonrelativistic potential energy is proposed.