On the axioms of topological electromagnetism

Delphenich, D. H.

doi:10.1002/andp.200510141

Cited by 29 publications

(35 citation statements)

References 21 publications

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“…A more logically defensible path would be to formulate the general laws without the introduction of a metric and then derive the appearance of the metric as a consequence of the way that electromagnetic waves propagate. The summary of this approach that follows is largely consistent with the work of Hehl and Obukhov [27], as well as the author [28].…”

Section: → ᒐᒉ(4) Such That T(v)(w) = T(w)(v) For All V W ∈ ‫ޒ‬supporting

confidence: 71%

“…5 Pre-metric electromagnetism [24][25][26][27][28] An early observation of Kottler [24] and Cartan [25] concerning the mathematical structure of Maxwell's equations for electromagnetism was that the only place that the spacetime metric played an essential role was in the definition of what is now called the Hodge star isomorphism, as it is applied to 2-forms. The possibility that one could introduce such an isomorphism independently of the introduction of a spacetime metric was further developed by Van Dantzig [26] in a manner that suggested that the fundamental spacetime structure in the eyes of electromagnetism was not a Lorentzian pseudometric on the tangent bundle, but an electromagnetic constitutive law on the bundle of 2-forms.…”

Section: → ᒐᒉ(4) Such That T(v)(w) = T(w)(v) For All V W ∈ ‫ޒ‬mentioning

confidence: 99%

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Symmetries and pre-metric electromagnetism

Delphenich

2005

Ann. Phys.

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The equations of pre-metric electromagnetism are formulated as an exterior differential system on the bundle of exterior differential 2-forms over the spacetime manifold. The general form for the symmetry equations of the system is computed and then specialized to various possible forms for an electromagnetic constitutive law, namely, uniform linear, non-uniform linear, and uniform nonlinear. It is shown that in the uniform linear case, one has four possible ways of prolonging the symmetry Lie algebra, including prolongation to a Lie algebra of infinitesimal projective transformations of a real four-dimensional projective space. In the most general non-uniform linear case, the effect of non-uniformity on symmetry seems inconclusive in the absence of further specifics, and in the uniform nonlinear case, the overall difference from the uniform linear case amounts to a deformation of the electromagnetic constitutive tensor by the electromagnetic field strengths, which induces a corresponding deformation of the symmetry Lie algebra that was obtained in the linear uniform case.

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Section: → ᒐᒉ(4) Such That T(v)(w) = T(w)(v) For All V W ∈ ‫ޒ‬supporting

confidence: 71%

Section: → ᒐᒉ(4) Such That T(v)(w) = T(w)(v) For All V W ∈ ‫ޒ‬mentioning

confidence: 99%

Symmetries and pre-metric electromagnetism

Delphenich

2005

Ann. Phys.

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“…A straightforward, but tedious, computation using a general matrix C partitioned into block form gives that C must be of the form: 18) in which A, B ∈GL(3; ‫. )ޒ‬ We can associate any such C with a unique element of GL(3; ‫)ރ‬ by way of the assignment: 19) which is also a group isomorphism onto. Hence, the subgroup of GL(6; ‫)ޒ‬ that preserves the complex structure defined by * is isomorphic to GL(3; ‫.…”

Section: The Action Of Gl(mentioning

confidence: 99%

Projective geometry and special relativity

Delphenich¹

2006

Ann. Phys.

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Some concepts of real and complex projective geometry are applied to the fundamental physical notions that relate to Minkowski space and the Lorentz group. In particular, it is shown that the transition from an infinite speed of propagation for light waves to a finite one entails the replacement of a hyperplane at infinity with a light cone and the replacement of an affine hyperplane -or rest space -with a proper time hyperboloid. The transition from the metric theory of electromagnetism to the pre-metric theory is discussed in the context of complex projective geometry, and ultimately, it is proposed that the geometrical issues are more general than electromagnetism, namely, they pertain to the transition from point mechanics to wave mechanics.

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“…The symmetry and topological concepts inherent in field theories have been analysed using this duality [1][2][3][4]. In fact, this duality has been thoroughly studied and many interesting physical consequences arising from this duality have also been analysed [5][6][7][8][9][10][11][12][13]. It is known that electrodynamics is dual under Hodge star operation, * F μν = − μντρ F μν /2.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric duality in superloop space

Faizal

Tsun

2015

Eur. Phys. J. C

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In this paper we constructed superloop space duality for a four dimensional supersymmetric Yang-Mills theory with N = 1 supersymmetry. This duality reduces to the ordinary loop space duality for the ordinary Yang-Mills theory. It also reduces to the Hodge duality for an abelian gauge theory. Furthermore, the electric charges, which are the sources in the original theory, appear as monopoles in the dual theory. Whereas, the magnetic charges, which appear as monopoles in the original theory, become sources in the dual theory.

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On the axioms of topological electromagnetism

Cited by 29 publications

References 21 publications

Symmetries and pre-metric electromagnetism

Symmetries and pre-metric electromagnetism

Projective geometry and special relativity

Supersymmetric duality in superloop space

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