In a series of papers,Quesne and Tkachuk (2006) presented a D+ 1-dimensional (𝛽, 𝛽')-two-parameter Lorentz-covariant deforme dalgebra which leads to a nonzero minimal measurable length. In this paper, the Lagrangian formulation of electrodynamics in a 3+1-dimensional spacetime described by Quesne-Tkachuk algebra is studied in the special case of 𝛽' = 2𝛽 up to the first order over the deformation parameter 𝛽. It is demonstrated that at the classical level there is a similarity between electrodynamics in the presence of a minimal measurable length (generalized electrodynamics) and Lee-Wick electrodynamics.We obtain the free space solutions of the inhomogeneous Maxwell’s equations in the presence of a minimal length. These solutions describe two vector particles (a massless vector particle and a massive vector particle). We estimate two different upper bounds on the isotropic minimal length. The first upper bound is near to the electroweak length scale (ℓelectroweak ∼ 10−18 m), while the second one is near to the length scale for the strong interactions (ℓstrong 10−15 m).The relationship between the Gaete-Spallucci nonlocal electrodynamics (2012) and electrodynamics with a minimal length is investigated.
