New electromagnetic conservation laws

Bergqvist, Göran; Eriksson, Ingemar; Senovilla, José M. M.

doi:10.1088/0264-9381/20/13/313

Cited by 27 publications

(53 citation statements)

References 12 publications

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“…However, the tensor versions are of varying degrees of difficulty: the familiar Bel-Robinson identity in Theorem 2a requires considerable preliminary work to establish lemmas for the Weyl tensor, and Theorem 2d requires Theorem 2a together with a number of other lemmas, one involving a 'mixed' identity. The tensor derivation of the new conservation law for electromagnetism [5] given in Section 7 also requires 'mixed' ddis. These tensor derivations are very complicated, and one wonders how long it would have taken to even conjecture the results in Theorems 2d and 6 without the parallel spinor (or null vector) results; but it seems that there is no easier signature-free way in tensors, and we should train ourselves to recognise such structures in tensors.…”

Section: Discussionmentioning

confidence: 99%

“…Recently Bergqvist, Eriksson and Senovilla [5] have used the spinor equivalent of the Chevreton tensor and given two interesting properties in curved space for source-free Einstein-Maxwell fields:…”

Section: Tensor Derivation Of New Electromagnetic Conservation Lawmentioning

confidence: 99%

“…The first of these properties is just a special case of the result previously derived in tensors for Lanczos candidates in 4-dimensional spaces [15], and given at the end of Section 4. The second property was deduced from the spinor form of the divergence of C abcd and Bergqvist, Eriksson and Senovilla [5] remark that the proof of this result is far from obvious from the tensor point of view. We shall now demonstrate that the result in [5] can be obtained in a direct and straightforward manner -until the complication at the last stages where two fddis valid in four dimensions have to be used explicitly.…”

Section: Tensor Derivation Of New Electromagnetic Conservation Lawmentioning

confidence: 99%

“…Senovilla [3] has demonstrated that a much larger class of tensors -superenergy tensors -share most of the desirable properties of the Bel-Robinson tensor, and Bergqvist [4] has shown how superenergy spinors give a simpler and more efficient presentation of certain aspects of these superenergy tensors. Recently, Bergqvist, Eriksson and Senovilla [5] have obtained new conservation laws for the electromagnetic field using superenergy spinor considerations, and emphasised that the proof of this result is far from obvious from the tensor point of view. It is reassuring to know that certain important but perhaps unexpected properties -disguised in the complexities of the tensor formalism -become more transparent in the spinor formalism; but the parallel and more transparent spinor investigations are restricted to 4-dimensional spacetimes with Lorentz signature, and so this assistance is not available in higher dimensions nor in four dimensional spaces with other signatures.…”

Section: Introductionmentioning

confidence: 99%

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Old and new results for superenergy tensors from dimensionally dependent tensor identities

Edgar

Wingbrant

2003

Journal of Mathematical Physics

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Abstract.It is known that some results for spinors, and in particular for superenergy spinors, are much less transparent and require a lot more effort to establish, when considered from the tensor viewpoint. In this paper we demonstrate how the use of dimensionally dependent tensor identities enables us to derive a number of 4-dimensional identities by straightforward tensor methods in a signature independent manner. In particular, we consider the quadratic identity for the Bel-Robinson tensor T abcx T abcy = δ y x T abcd T abcd /4 and also the new conservation laws for the Chevreton tensor, both of which have been obtained by spinor means; both of these results are rederived by tensor means for 4-dimensional spaces of any signature, using dimensionally dependent identities, and also we are able to conclude that there are no direct higher dimensional analogues. In addition we demonstrate a simple way to show non-existense of such identities via counter examples; in particular we show that there is no non-trivial Bel tensor analogue of this simple Bel-Robinson tensor quadratic identity. On the other hand, as a sample of the power of generalising dimensionally dependent tensor identities from four to higher dimensions, we show that the symmetry structure, trace-free and divergence-free nature of the four dimensional Bel-Robinson tensor does have an analogue for a class of tensors in higher dimensions. It is reassuring to know that certain important but perhaps unexpected properties -disguised in the complexities of the tensor formalism -become more transparent in the spinor formalism; but the parallel and more transparent spinor investigations are restricted to 4-dimensional spacetimes with Lorentz signature, and so this assistance is not available in higher dimensions nor in four dimensional spaces with other signatures. Deser [6] has emphasised the significance of the Bel-Robinson tensor in higher dimensions, and one of the important features of Senovilla's method of construction of superenergy tensors [3] is that it is applicable to arbitrary fields in any dimension; and so, for higher dimensions, it becomes an obvious concern whether there could be unexpected properties for superenergy tensors -disguised in the even deeper complexities of tensor formalism in higher dimensions -analogous to those properties revealed by spinor formalism in four dimensions. Deeper investigations into the interaction between dimension and tensor identities have been instrumental in illustrating the uniqueness of some of the Bel-Robinson tensor's properties in four dimensions [6], explaining

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Section: Discussionmentioning

confidence: 99%

Section: Tensor Derivation Of New Electromagnetic Conservation Lawmentioning

confidence: 99%