Is it possible to accommodate massive photons in the framework of a gauge-invariant electrodynamics?

Fonseca, M. V. S.; Paredes, A.V

doi:10.1590/s0103-97332010000300011

Cited by 10 publications

(6 citation statements)

References 10 publications

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“…Although this problem can successfully be solved using the Stückelberg mechanism [23] and other methods (e.g., Podolsky Electrodynamics cf. [24]) which are usually descendants of the original Stückelberg mechanism, these methods usually introduce new scalar particles.…”

Section: Discussionmentioning

confidence: 99%

Gauge Invariant Massive Long Range and Long Lived Photons

Nyambuya¹

2014

JMP

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Prevailing and conventional wisdom holds that intermediate gauge Bosons for long range interactions such as the gravitational and electromagnetic interactions must be massless as is assumed to be the case for the photon which mediates the electromagnetic interaction. We have argued in a different reading that it should in-principle be possible to have massive photons. The problem of whether or not these photons will lead to short or long range interactions has not been answered. Naturally, because these photons are massive, one would without much pondering and excogitation on the matter assume that these photons can only take part in short range interactions. Contrary to this and to conventional wisdom; via a subtlety-namely, the foregoing of the Lorenz gauge and in line with ideas set out in out proposed Unified Field Theory, the introduction of a vector potential whose components are 4 × 4 Hermitian matrices; we show within the confines of Proca Electrodynamics under the said modifications that massive photons should be long lived (i.e., stable) and be able to take part in long range interactions without any problem.

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Section: Discussionmentioning

confidence: 99%

Gauge Invariant Massive Long Range and Long Lived Photons

Nyambuya¹

2014

JMP

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“…where a :=h √ 2β . Equation (26) is the Lagrangian density originally introduced by Podolsky [30][31][32][33], and a is called Podolsky's characteristic length [34][35][36][37][38]. The Euler-Lagrange equation for the Lagrangian density (25) is [39,40]…”

Section: Lagrangian Formulation Of Electrodynamics With An External Smentioning

confidence: 99%

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

Moayedi

Setare

Khosropour

2013

Advances in High Energy Physics

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In a series of papers, Quesne and Tkachuk (J. Phys. A: Math. Gen. 39, 10909 (2006); Czech. J. Phys. 56, 1269Phys. 56, (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 β ′ = 2β up to 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 (J. Phys. A: Math. Theor. 45, 065401 (2012)) and electrodynamics with a minimal length is investigated.

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“…where a := h√ 2β is a constant parameter which is called Podolsky's characteristic length [37][38][39][40][41]. The Euler-Lagrange equation for the Lagrangian density ( 30) is [42][43][44]…”

Section: Modified Commutation Relations With a Minimal Length Scalementioning

confidence: 99%

Lagrangian Formulation of a Magnetostatic Field in the Presence of a Minimal Length Scale Based on the Kempf Algebra

Moayedi

Setare

Khosropour

2013

Int. J. Mod. Phys. A

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In the 1990s, Kempf and his collaborators Mangano and Mann introduced a D-dimensional (β, β ′ )-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length (△X i ) min =h √ Dβ + β ′ , ∀i ∈ {1, 2, · · · , D}. In this work, the Lagrangian formulation of a magnetostatic field in three spatial dimensions (D = 3) described by Kempf algebra is presented in the special case of β ′ = 2β up to the first order over β. We show that at the classical level there is a similarity between magnetostatics in the presence of a minimal length scale (modified magnetostatics) and the magnetostatic sector of the Abelian Lee-Wick model in three spatial dimensions. The integral form of Ampere's law and the energy density of a magnetostatic field in the modified magnetostatics are obtained. Also, the Biot-Savart law in the modified magnetostatics is found. By studying the effect of minimal length corrections to the gyromagnetic moment of the muon, we conclude that the upper bound on the isotropic minimal length scale in three spatial dimensions is 4.42 × 10 −19 m. The relationship between magnetostatics with a minimal length and the Gaete-Spallucci non-local magnetostatics (J. Phys. A: Math. Theor. 45, 065401 (2012)) is investigated.

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Is it possible to accommodate massive photons in the framework of a gauge-invariant electrodynamics?

Cited by 10 publications

References 10 publications

Gauge Invariant Massive Long Range and Long Lived Photons

Gauge Invariant Massive Long Range and Long Lived Photons

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

Lagrangian Formulation of a Magnetostatic Field in the Presence of a Minimal Length Scale Based on the Kempf Algebra

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