A brief study on the transformation of Maxwell equations in Euclidean four-space

Zampino, E.J.

doi:10.1063/1.527137

Cited by 9 publications

(18 citation statements)

References 5 publications

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“…Since these assumptions on signs are postulated in Maxwell's electrodynamics all together 'at the same time', it seems to be impossible to find out relations between them. Earlier discussions of Maxwell's theory with Euclidean signature were given by Zampino [27] and on the Euclidean Maxwell-Einstein equations by Brill [2]. Both authors didn't use the premetric approach, even though Brill mentions it.…”

Section: Introductionmentioning

confidence: 99%

Is the Lorentz signature of the metric of spacetime electromagnetic in origin?

Itin

Hehl

2004

Annals of Physics

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We formulate a premetric version of classical electrodynamics in terms of the excitation H = (H, D) and the field strength F = (E, B). A local, linear, and symmetric spacetime relation between H and F is assumed. It yields, if electric/magnetic reciprocity is postulated, a Lorentzian metric of spacetime thereby excluding Euclidean signature (which is, nevertheless, discussed in some detail). Moreover, we determine the Dufay law (repulsion of like charges and attraction of opposite ones), the Lenz rule (the relative sign in Faraday's law), and the sign of the electromagnetic energy. In this way, we get a systematic understanding of the sign rules and the sign conventions in electrodynamics. The question in the title of the paper is answered affirmatively.

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Section: Introductionmentioning

confidence: 99%

Is the Lorentz signature of the metric of spacetime electromagnetic in origin?

Itin

Hehl

2004

Annals of Physics

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“…Interestingly, we show that Φ K has the same structural form that the scalar potential (in the associated Lorenz condition) of an electromagnetic theory formulated in the Euclidean four-space [4]. We also show that the vector potential in the Kirchhoff gauge A K satisfies a wave equation with a nonlocal source.…”

Section: Introductionmentioning

confidence: 79%

“…Euclidean fields are seen to satisfy an Euclidean version of Maxwell's equations which was discussed some years ago by Zampino [4] and Brill [5] and more recently by the author [6], kobe [7] and Itin and Hehl [8]. In vector notation the Euclidean equations can be written as…”

Section: The Kirchhoff Gaugementioning

confidence: 99%

“…When ρ = 0 the solutions of Eq. (6) are either exponentially growing or decaying functions [4]. On the other hand, Eq.…”

Section: The Kirchhoff Gaugementioning

confidence: 99%

“…An alternative interpretation for Φ K An alternative interpretation for the potential Φ K may be obtained from an electromagnetic theory formulated in an Euclidean four-space [4]. As is well-known, the Maxwell equations essentially fix the spacetime signature to be Lorentzian.…”

Section: The Kirchhoff Gaugementioning

confidence: 99%

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The Kirchhoff gauge

Heras

2006

Annals of Physics

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We discuss the Kirchhoff gauge in classical electrodynamics. In this gauge the scalar potential satisfies an elliptical equation and the vector potential satisfies a wave equation with a nonlocal source. We find the solutions of both equations and show that, despite of the unphysical character of the scalar potential, the electric and magnetic fields obtained from the scalar and vector potentials are given by their well-known retarded expressions. We note that the Kirchhoff gauge pertains to the class of gauges known as the velocity gauge.

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The Spacetime Algebra Approach to Massive Classical Electrodynamics with Magnetic Monopoles

Cafaro

Ali

2006

AACA

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Maxwell's equations with massive photons and magnetic monopoles are formulated using spacetime algebra. It is demonstrated that a single nonhomogeneous multi-vectorial equation describes the theory. Two limiting cases are considered and their symmetries highlighted: massless photons with magnetic monopoles and finite photon mass in the absence of monopoles. Finally, it is shown that the EM-duality invariance is a symmetry of the Hamiltonian density (for Minkowskian spacetime) and Lagrangian density (for Euclidean 4-space) that reflects the signature of the respective metric manifold.

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A brief study on the transformation of Maxwell equations in Euclidean four-space

Abstract: Electromagnetic-type fields in Euclidean four-space are studied by changing the sign of the time differential term in Faraday’s law of induction. Although a covariant set of field equations can be derived, difficulties arise in the case of time-dependent fields.

Cited by 9 publications

References 5 publications

Is the Lorentz signature of the metric of spacetime electromagnetic in origin?

Is the Lorentz signature of the metric of spacetime electromagnetic in origin?

The Kirchhoff gauge

The Spacetime Algebra Approach to Massive Classical Electrodynamics with Magnetic Monopoles

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