Formulation of Electrodynamics with an External Source in the Presence of a Minimal Measurable Length
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 Quesn...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2013/657870 |
| Summary: | 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 (
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. |
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| ISSN: | 1687-7357 1687-7365 |