Formulation of Electrodynamics with an External Source in the Presence of a Minimal Measurable Length

Abstract EN

In a series of papers, Quesne and Tkachuk (2006) presented a D + 1-dimensional (β, β′)-two-parameter Lorentz-covariant deformed algebra 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.