YES! We introduce a variable power Maxwell nonlinear electrodynamics theory which can remove the singularity of electric field of point-like charges at their locations. One of the main problems of Maxwell's electromagnetic field theory is related to the existence of singularity for electric field of point-like charges at their locations. In other words, the electric field of a point-like charge diverges at the charge location which leads to an infinite self-energy. In order to remove this singularity a few nonlinear electrodynamics (NED) theories have been introduced. Born-Infeld (BI) NED theory is one of the most famous of them. However the power Maxwell (PM) NED cannot remove this singularity. In this paper, we show that the PM NED theory can remove this singularity, when the power of PM NED is less than $s<\frac{1}{2}$.
On some nonlinear extensions to Maxwell's electrodynamics
Laboratoire de Physique et Chimie Théoriques, Université de Lorraine – CNRS（洛林大学-法国国家科学研究中心理论与化学物理实验室）；Departamento de Física, Colegio de Ciencias e Ingeniería, Universidad San Francisco de Quito（基多圣弗朗西斯科大学科学与工程学院物理系）
An electric charge has no screw sense--a comment on the twistfree formulation of electrodynamics by da Rocha & Rodrigues
Da Rocha和Rodigues（RR）声称：（i）在经典电动力学中，矢量演算中对极矢量和轴矢量的区分，以及外部演算中对扭转和非扭转形式的区分是不适当的和多余的;（ii）他们可以从麦克斯韦方程组导出洛伦兹力方程。对于（i），我们指出，极性/轴向和扭转/非扭转的区别来自于电荷是纯标量的性质，即不携带任何螺旋感。因此，上述区别是电动力学任何基本理论的必要组成部分。如果将允许的坐标变换限制为具有正雅可比行列式的坐标变换（或规定一个等价的约束），则RR方案可以被容纳;然而，这样的限制是非法的，因为电动力学实际上在具有负雅可比行列式的变换下也是协变的。关于（ii）从麦克斯韦方程组“推导”洛伦兹力，我们指出RR首先忘记了给麦克斯韦方程组中的符号F（场强）一个运算意义。他们的证据是空的。总结：RR的方法并没有给电动力学的结构带来任何新的见解。
