The spin Hall effect of electromagnetic wave has important application prospects in the fields of Optical-electromechanical conversion, condensed matter and high energy physics. Based on the Euler–Lagrange equations of electromagnetic field by four-dimensional covariation, a deflection model of electromagnetic wave reflecting and refracting on interface of media is established in this paper. By using Lie group analysis method, the allowable infinitesimal symmetries, conserved quantities of partial differential equations and motion equation of energy center are derived. More importantly, their detailed analytical expressions and properties are given. The content of this paper can reveal the mechanism and influencing factors for transverse shift of the electromagnetic wave energy center, and provide a powerful theoretical basis for the numerical simulation of nonlinear photoelectric wave equation and spin regulation.

中文翻译：

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介质界面电磁波横向位移的李群分析方法

电磁波的自旋霍尔效应在光电转换，凝聚态和高能物理领域具有重要的应用前景。基于二维协变的电磁场欧拉-拉格朗日方程，建立了电磁波在介质界面反射和折射的偏转模型。利用李群分析法，推导了能量中心的容许无穷小对称性，偏微分方程的守恒量和运动方程。更重要的是，给出了它们的详细分析表达式和性质。本文的内容可以揭示电磁波能量中心横向移动的机理和影响因素，