电磁场的流体动力学构造
Hydrodynamic construction of the electromagnetic field
摘要：
本文提出了一种新的电磁场欧拉流体力学模型，其中Maxwell \s方程中的离散矢量指数被连续的角自由度所取代，并发展了相应的拉格朗日图像，其中流体粒子具有旋转和平移自由度。这使我们能够将先前为自旋0系统提出的状态构造的精确方法扩展到电磁场，其中依赖于时间的波函数是从确定性轨迹的单值连续体计算的，其中两个时空点最多由单个轨道连接。将自旋为0的理论推广到一般的黎曼流形上，导出了连续介质力学中的Maxwell \s方程组，并将电磁结构作为其特例.特别地，对于大质量系统，平空间麦克斯韦方程组被表示为弯曲空间的薛定谔方程。欧拉场论的洛伦兹协变性是作为一种集体效应从非协变的拉格朗日坐标模型中得到的。该方法体现了Maxwell \s方程中隐含的量子势的电磁模拟。这意味着麦克斯韦\s方程的\classical极限的一个新定义，不同于几何光学。结果表明，麦克斯韦\s方程可以通过经典模型的正则量子化得到。利用经典轨迹导出了欧拉图像中电磁场传播子的新表达式。的轨迹和传播的解决方案的方法示出的情况下，光波。
英文摘要：
We present an alternative Eulerian hydrodynamic model for the electromagnetic field in which the discrete vector indices in Maxwell\s equations are replaced by continuous angular freedoms, and develop the corresponding Lagrangian picture in which the fluid particles have rotational and translational freedoms. This enables us to extend to the electromagnetic field the exact method of state construction proposed previously for spin 0 systems, in which the time-dependent wavefunction is computed from a single-valued continuum of deterministic trajectories where two spacetime points are linked by at most a single orbit. The deduction of Maxwell\s equations from continuum mechanics is achieved by generalizing the spin 0 theory to a general Riemannian manifold from which the electromagnetic construction is extracted as a special case. In particular, the flat-space Maxwell equations are represented as a curved-space Schrödinger equation for a massive system. The Lorentz covariance of the Eulerian field theory is obtained from the non-covariant Lagrangian-coordinate model as a kind of collective effect. The method makes manifest the electromagnetic analogue of the quantum potential that is tacit in Maxwell\s equations. This implies a novel definition of the \classical limit\ of Maxwell\s equations that differs from geometrical optics. It is shown that Maxwell\s equations may be obtained by canonical quantization of the classical model. Using the classical trajectories a novel expression is derived for the propagator of the electromagnetic field in the Eulerian picture. The trajectory and propagator methods of solution are illustrated for the case of a light wave.
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