标题： 电磁学中的协变跃迁条件 显示英文标题

标题： Covariant jump conditions in electromagnetism

摘要： 在任意材料介质中，麦克斯韦电动力学的广义协变四维表示可以在无度规的电磁理论形式中直接实现。 在此设置中，由两个满足麦克斯韦方程的张量场描述的电磁现象。 这些场之间的通用张量本构关系是该理论的一个独立要素。 通过使用不同的本构关系（局部和非局部、线性和非线性等），可以覆盖广泛的应用领域。 在本文中，我们给出了两种介质之间任意运动表面上的场和能量动量张量的跃迁条件。 从微分和积分形式的麦克斯韦方程出发，我们推导出与任何度规和联络无关的协变边界条件。 这些条件包括协变定义的表面电流，并适用于任意运动的光滑曲边界表面。 作为所提出跃迁公式的应用，我们推导出一种洛伦兹型度规，作为各向同性介质中波前存在的条件。 这一结果既适用于普通材料，也适用于具有负材料常数的超材料。 显示英文摘要

摘要： A generally covariant four-dimensional representation of Maxwell's electrodynamics in a generic material medium can be achieved straightforwardly in the metric-free formulation of electromagnetism. In this setup, the electromagnetic phenomena described by two tensor fields, which satisfy Maxwell's equations. A generic tensorial constitutive relation between these fields is an independent ingredient of the theory. By use of different constitutive relations (local and non-local, linear and non-linear, etc.), a wide area of applications can be covered. In the current paper, we present the jump conditions for the fields and for the energy-momentum tensor on an arbitrarily moving surface between two media. From the differential and integral Maxwell equations, we derive the covariant boundary conditions, which are independent of any metric and connection. These conditions include the covariantly defined surface current and are applicable to an arbitrarily moving smooth curved boundary surface. As an application of the presented jump formulas, we derive a Lorentzian type metric as a condition for existence the wave front in isotropic media. This result holds for the ordinary materials as well as for the metamaterials with the negative material constants.