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arXiv 0903.5520hep-th
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论预度规电动力学中的光传播。协变色散关系

On light propagation in premetric electrodynamics. Covariant dispersion relation

Yakov Itin

摘要:

电动力学的预度量方法提供了一个广泛的电磁现象的统一描述。特别是,它涉及到轴子,轴子和skewon修改的经典电动力学。当考虑电磁张量和爱因斯坦-嘉当引力挠率之间的非最小耦合时,也会出现这种形式。此外,预度量形式可以作为各向异性介质的电磁特性的一般协变背景。本文研究了预度规电动力学中的波传播问题。我们推导出一个系统的特征方程对应的预度量推广的麦克斯韦方程。这个奇异系统的特征在于伴随矩阵变成一个非常特殊的形式-比例的标量四次因子。我们证明了特征系统存在非平凡解的必要条件是由唯一的标量色散关系表示的。在切向(动量)空间中,它确定了一个四阶光超曲面,它取代了标准麦克斯韦理论中的普通光锥。本文导出了协变色散关系的一种显式形式,并建立了它的数学模型和物理根源。

英文摘要:

The premetric approach to electrodynamics provides a unified description of a wide class of electromagnetic phenomena. In particular, it involves axion, dilaton and skewon modifications of the classical electrodynamics. This formalism emerges also when the non-minimal coupling between the electromagnetic tensor and the torsion of Einstein-Cartan gravity is considered. Moreover, the premetric formalism can serve as a general covariant background of the electromagnetic properties of anisotropic media. In the current paper, we study wave propagation in the premetric electrodynamics. We derive a system of characteristic equations corresponded to premetric generalization of the Maxwell equation. This singular system is characterized by the adjoint matrix which turns to be of a very special form -- proportional to a scalar quartic factor. We prove that a necessary condition for existence a non-trivial solution of the characteristic system is expressed by a unique scalar dispersion relation. In the tangential (momentum) space, it determines a fourth order light hypersurface which replaces the ordinary light cone of the standard Maxwell theory. We derive an explicit form of the covariant dispersion relation and establish it'salgebraic and physical origin.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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