In this paper the Proca field equations for a massive gauge particle are obtained in the presence of a natural momentum cutoff “ ” based on a covariant generalization of a one-parameter extension of the Heisenberg algebra. The Yukawa potential for a static point source in the presence of (generalized Yukawa potential) is obtained analytically and it is shown that in contrast with the Yukawa potential for a static point source in Proca electrodynamics, the generalized Yukawa potential has a finite value at the location of the static point source. Our calculations demonstrate that the Coulomb potential, the Yukawa potential, and the Coulomb potential in the presence of can be derived from the generalized Yukawa poitential. We show that the free space solutions of Proca electrodynamics in the presence of describe a massive gauge particle with the effective mass , where is the rest mass of the ordinary Proca particle. Numerical estimations in Sect. 5, show that the lower bound for must take the value in order to avoid complex values for the effective mass . This lower bound for is near to the momentum scale of the electroweak interactions. It should be mentioned that for the very large values of the results of this work reduce to the well-known results of standard Proca electrodynamics.
