Is it possible to describe an electron by the evolution of a single point?

TL;DR

The paper constructs a classical relativistic model in which the electron is described by the time evolution of the center of charge $\mathbf{r}$ and is governed by a Lagrangian depending on $\mathbf{u}$, $\mathbf{a}$ and the attached frame, giving a fourth-order dynamics compatible with Dirac theory upon quantization. A separate center of mass $\mathbf{q}$ exists and the spin and magnetic properties arise from the CC–CM relative motion (zitterbewegung), with $\mathbf{u}=d\mathbf{r}/dt=c$ and $|\mathbf{v}|<c$, giving $H=\gamma(v)mc^2$ and $\mathbf{p}=\gamma(v)m\mathbf{v}$. The model yields Pauli-Lubanski invariants and two angular momenta $\mathbf{S}$ and $\mathbf{S}_{\mathrm{CM}}$, reproducing Dirac spin in the CM frame and linking the internal structure to a constant separation $R_0$ that encodes $\hbar$. In sum, the work provides a geometrical, group-theoretic classical framework for relativistic spinning particles, illuminating how spin and related observables emerge from CC–CM dynamics and offering insights into spin-affected phenomena such as spin-polarized tunneling and bound states.

Abstract

The answer to the title-question is positive. The analysis of the geometry of continuous and differentiable curves in three-dimensional Euclidean space suggests that the point represents the location of the center of charge of the electron, satisfies a system of ordinary differential equations of fourth order, and moves at the speed of light. The center of mass of the electron is a different point and will be determined by the evolution of the center of charge. It is the relative motion of the center of charge around the center of mass that gives rise to the spin and magnetic properties.