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Recently a one-parameter extension of the covariant Heisenberg algebra withthe extension parameter $l$ ($l$ is a non-negative constant parameter which hasa dimension of $[momentum]^{-1}$) in a $(D+1)$-dimensional Minkowski space-timehas been presented [G. P. de Brito, P. I. C. Caneda, Y. M. P. Gomes, J. T.Guaitolini Junior and V. Nikoofard, Effective models of quantum gravity inducedby Planck scale modifications in the covariant quantum algebra, Adv. HighEnergy Phys. 2017 (2017) 4768341]. The Abelian Proca model is reformulated fromthe viewpoint of the above one-parameter extension of the covariant Heisenbergalgebra. It is shown that the free space solutions of the above modified Procamodel satisfy the modified dispersion relation$\frac{\textbf{p}^2}{\left(1+\frac{\Lambda^2}{2\hbar^2}\textbf{p}^2\right)^2}=m^2c^2$where $\Lambda=\hbar l$ is the characteristic length scale in our model. Thismodified dispersion relation describes two massive vector particles with theeffective masses ${\calM}_{_\pm}(\Lambda)=\frac{2m}{1\mp\sqrt{1-2\left(\frac{mc\Lambda}{\hbar}\right)^2}}$.Numerical estimations show that the maximum value of $\Lambda$ in afour-dimensional space-time is near to the electroweak length scale, i.e.,$\Lambda_{_{max}}\sim l_{_{electroweak}}\sim10^{-18}\; m$. We show that in theinfrared/large-distance domain the modified Proca model behaves like an Abelianmassive Lee-Wick model which has been presented by Accioly and his co-workers[A. Accioly, J. Helayel-Neto, G. Correia, G. Brito, J. de  Almeida and W. Herdy, Interparticle potential energy for D-dimensionalelectromagnetic models from the corresponding scalar ones, Phys. Rev. D 93(2016) 105042].

The Ultraviolet and Infrared Behavior of an Abelian Proca Model From the Viewpoint of a One-Parameter Extension of the Covariant Heisenberg Algebra