Invariants of the electromagnetic field

Escobar, C. A.; Urrutia, L. F.

doi:10.1063/1.4868478

Cited by 15 publications

(14 citation statements)

References 6 publications

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“…As we will use the fields D and H to describe the dynamics of the theory, we need their time development. The time development of the D field is directly determined by Ampère's law (21). In order to extract the time development of H from Faraday's law (23), it is necessary to use the constitutive relations (18).…”

Section: First-order Formulation Of Nonlinear Electrodynamicsmentioning

confidence: 99%

Degenerate behavior in nonlinear vacuum electrodynamics

Escobar¹,

Potting²

2020

Phys. Scr.

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We study nonlinear vacuum electrodynamics in the first-order formulation proposed by Plebański. We analyze in detail the equations of motion, and identify conditions for which a singularity can occur for the time derivative of one of the field components. The resulting degenerate behavior can give rise to a shock wave with a reduction of the local number of degrees of freedom. We use an example model to illustrate the occurrence of superluminal propagation for field values approaching the singularity.

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Section: First-order Formulation Of Nonlinear Electrodynamicsmentioning

confidence: 99%

Degenerate behavior in nonlinear vacuum electrodynamics

Escobar¹,

Potting²

2020

Phys. Scr.

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“…Studies on nonlinear electrodynamics (NLED) have a long history in physics and dates back from 1934 when Born and Infeld [1] proposed a nonlinear modification of Maxwell theory with the aim to correct the infinities of the selfenergy and the fields of a point charge. Such model is constructed from the only Lorentz electromagnetic invariants F = F µν F µν and G = F µν F µν [2] and it has been shown that it can be derived as an effective action from quantized string theory [3]. As a second well known nonlinear electrodynamics example we found the Heisenberg and Euler model [4], which is capable of explaining scattering processes between photons and creation of electron-positron pairs.…”

Section: Introductionmentioning

confidence: 93%

Hamiltonian analysis of ModMax nonlinear electrodynamics in the first order formalism

Escobar,

Linares,

Tlatelpa-Mascote

2021

Preprint

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In this work we study the so-called ModMax nonlinear electrodynamics, which is a novel model designed to preserve duality rotations and conformal transformations, such as the Maxwell's equations do. This model allows to study diverse gravitational phenomena when is coupled to General Relativity, in particular charged black holes and gravitational waves. In the present work we focus in the dynamics and Hamiltonian analysis of the model. Specifically, we analyze the propagation of the discontinuities of the field and obtain the corresponding dispersion relations. To perform the Hamiltonian analysis we adopt the first order formalism develop by Plebański and follow the Dirac method for theories with constraints. We derive the effective Hamiltonian, classify all the constraints and identify the degrees of freedom. We prove that the effective Hamiltonian is strictly bounded from below and investigate the existence of non trivial minima.

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“…The argument is straightforward. Any gauge and Poincaré invariant quantity built out of the electromagnetic vector potential A µ and its field strength F µν alone may be constructed out of only [6] the following two well-known gauge invariant and Lorentz scalar or pseudo-scalar quantities,…”

Section: Introductionmentioning

confidence: 99%

Deformed Hopfion-Rañada Knots in ModMax Electrodynamics

Dassy¹,

Govaerts²

2021

Preprint

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Source-free so-called ModMax theories of nonlinear electrodynamics in the four dimensional Minkowski spacetime vacuum are the only possible continuous deformations -and as a function of a single real and positive parameter -of source-free Maxwell linear electrodynamics in the same vacuum, which preserve all the same Poincaré and conformal spacetime symmetries as well as the continuous duality invariance of Maxwell's theory. Null field configurations of the latter however, including null electromagnetic knots, are singular for the Lagrangian formulation of any spacetime Poincaré and conformal invariant theory of nonlinear electrodynamics. In particular null hopfion-Rañada knots are a distinguished and fascinating class on their own of topologically nontrivial solutions to Maxwell's equations. This work addresses the fate of these configurations within ModMax theories. A doubled class of ModMax deformed hopfion-Rañada knots is thereby identified, each of which coalescing back in a continuous fashion to the original hopfion-Rañada knot when the nonlinear deformation parameter is turned off.

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Invariants of the electromagnetic field

Abstract: We present a constructive proof that, in electrodynamics, all of the gauge-invariant Lorentz scalars and pseudoscalars can be expressed as functions of the quadratic ones.

Cited by 15 publications

References 6 publications

Degenerate behavior in nonlinear vacuum electrodynamics

Degenerate behavior in nonlinear vacuum electrodynamics

Hamiltonian analysis of ModMax nonlinear electrodynamics in the first order formalism

Deformed Hopfion-Rañada Knots in ModMax Electrodynamics

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