Relativistic electrodynamics without Lorentz transformations

The object of this exercise is to show that the force between moving charges can be obtained in a very different way than is usual without recourse to the Lorentz transformations. We suppose the spinning electron creates two massless strings which connect to another electron either stationary or moving. Each string carries a wave, one the de Broglie wave and the other a wave that moves at c that mediates the force between charges in addition to guiding the electron’s motion.

Relativistic Electrodynamics

The concept of action is introduced using Lagrangian and Hamiltonian mechanics, and is used to describe the relativistic mechanics of a free particle: free particle canonical 4-momentum and angular momentum 4-tensor. The problem of a charged particle in an external field is considered in detail, resulting in the relativistic version of the Lorentz force law. The electromagnetic field is described using the action principle: The Lagrange density function and the recovery of Maxwell’s equations and charge conservation. The simplest Lagrangian density that can be constructed from a four-vector field is known as the “proca Lagrangian,” but it is shown to predict a massive photon. Finally, the canonical stress-energy tensor is derived along with conservation laws.

On a ‘time’ reparametrization in relativistic electrodynamics with travelling waves

We briefly report on our method [23] of simplifying the equations of motion of charged particles in an electromagnetic (EM) field that is the sum of a plane travelling wave and a static part; it is based on changes of the dependent variables and the independent one (light-like coordinate ξ instead of time t). We sketch its application to a few cases of extreme laser-induced accelerations, both in vacuum and in plane problems at the vacuum-plasma interface, where we are able to reduce the system of the (Lorentz-Maxwell and continuity) partial differential equations into a family of decoupled systems of Hamilton equations in 1 dimension. Since Fourier analysis plays no role, the method can be applied to all kind of travelling waves, ranging from almost monochromatic to socalled “impulses”.