满Minkowski时空中的电动力学及其在经典连续统电动力学中的应用
Electrodynamics in a Filled Minkowski Spacetime with Application to Classical Continuum Electrodynamics
摘要：
闵可夫斯基时空是研究真空中粒子和场的相对论动力学的一个方便的环境。为了研究发生在电介质或其他线性介质中的事件，我们采用了常见的连续介质假设，即折射率为n的线性、各向同性、均匀、透明介质填充了整个空间，并寻求适用于填充时空的相对性原理。应用爱因斯坦假设与c/n作为光速，我们展示了如何有效的信号速度的结果在适当的时间由折射率的缩放和检查的后果达朗贝尔的原则，拉格朗日方程，和规范的动量场。在充满时空的动力学原理，然后应用到电磁拉格朗日，我们推导出的运动方程是不变的材料洛伦兹变换。宏观场的动力学的新表示是一致的量子化宏观场的等时对易关系，量子-经典对应，叠加原理，电磁边界条件。
英文摘要：
Minkowski spacetime is a convenient setting for the study of the relativistic dynamics of particles and fields in the vacuum. In order to study events that occur in a dielectric or other linear medium, we adopt the familiar continuum assumption of a linear, isotropic, homogeneous, transparent medium of refractive index n filling all space and seek the principle of relativity that applies in the filled spacetime. Applying the Einstein postulates with c/n as the speed of light, we show how the effective signal velocity results in a scaling of the proper time by the refractive index and examine the consequences for D'Alembert's principle, the Lagrange equations, and the canonical momentum field. The principles of dynamics in the filled spacetime are then applied to the electromagnetic Lagrangian and we derive equations of motion that are invariant with respect to a material Lorentz transformation. The new representation of the dynamics of macroscopic fields is shown to be consistent with the equal-time commutation relation for quantized macroscopic fields, quantum--classical correspondence, the principle of superposition, and electromagnetic boundary conditions.
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