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Methodological notes

# Energy—momentum tensor of the electromagnetic field in dispersive media

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Peter the Great Saint-Petersburg Polytechnic University, ul. Polytechnicheskaya 29, St. Petersburg, 195251, Russian Federation

The relation is considered between the energy—momentum tensor of the electromagnetic field and the group velocity of quasi-monochromatic waves in a nonabsorbing, isotropic, temporally and spatially dispersive dielectric. It is shown that, in the absence of external charges and currents in the dielectric, when the Abraham momentum density is used, there is no need to introduce the Abraham force applied to matter for providing the fulfillment of the law of conservation of momentum. The energy—momentum tensor proves to be symmetric and the Maxwell stress tensor is expressed either in terms of the momentum density vector and group velocity or in terms of the energy density and group velocity. The stress tensor and energy density strongly depend on the frequency and wave vector derivatives from functions describing the electromagnetic properties of the medium (permittivity and magnetic permittivity). The results are applicable both for ordinary and left-handed media and are compared with the data obtained by other authors. The pressure produced by waves on the interface of two media is calculated. It is shown that in ordinary and left-handed media, either the light pressure or light attraction can appear depending on the parameters of media. The striction effect is taken into account for liquid dielectrics.

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Keywords: energy--momentum tensor, dispersive media, group velocity, light pressure, striction effect
PACS: 03.50.De, 41.20.−q, 77.22.−d (all)
DOI: 10.3367/UFNe.0186.201602c.0146
URL: https://ufn.ru/en/articles/2016/2/d/
Citation: Toptygin I N, Levina K "Energy—momentum tensor of the electromagnetic field in dispersive media" Phys. Usp. 59 141–152 (2016)
 BibTex BibNote ® (generic)BibNote ® (RIS)MedlineRefWorks %0 Journal Article %T Energy—momentum tensor of the electromagnetic field in dispersive media %A I. N. Toptygin %A K. Levina %I Physics-Uspekhi %D 2016 %J Phys. Usp. %V 59 %N 2 %P 141-152 %U https://ufn.ru/en/articles/2016/2/d/ %U https://doi.org/10.3367/UFNe.0186.201602c.0146

Received: 28th, February 2015, revised: 4th, December 2015, 15th, December 2015

Îðèãèíàë: Òîïòûãèí È Í, Ëåâèíà Ê «Òåíçîð ýíåðãèè-èìïóëüñà ýëåêòðîìàãíèòíîãî ïîëÿ â ñðåäàõ ñ äèñïåðñèåé» ÓÔÍ 186 146–158 (2016); DOI: 10.3367/UFNr.0186.201602c.0146

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