Formulation of Electrodynamics with an External Source in the Presence of a Minimal Measurable Length. (28th February 2013)

• Record Type: Journal Article
• Authors: Moayedi, S. K.; Setare, M. R.; Khosropour, B.
• Other Names: Scholtz Frederik G. Academic Editor.
• Is Part Of: Advances in high energy physics. Volume 2013(2013)
• Publication Date: 2013-02-28
• Subjects: Particles (Nuclear physics) -- Periodicals; Particles (Nuclear physics); Periodicals; 539.76
• DOI: 10.1155/2013/657870
• Languages: English
• ISSNs: 1687-7357

Abstract

Abstract : 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 ′ = 2 β 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 (ℓ electroweak ~ 10 −18 m), while the second one is near to the length scale for the strong interactions (ℓ strong ~ 10 −15 m). The relationship between the Gaete-Spallucci nonlocal electrodynamics (2012) and electrodynamics with a minimal length is investigated.