Simple classical model of spin membrane particle

TL;DR

This paper presents a classical, membrane-based model of elementary particles with finite size, charge, and spin, using non-linear electromagnetic fields and numerical solutions to describe particle properties.

Contribution

It introduces a novel classical model combining membrane structures, Kaluza-Klein Lagrangian, and non-linear fields to produce bounded particle states with quantized properties.

Findings

Derived solutions for particle-like states with finite mass, charge, and spin.

Calculated the fine structure constant within the model.

Obtained numerical solutions for various multipole configurations.

Abstract

In this paper I developed a classical model of elementary particle that is associated with a membrane of finite size, surrounded by non-linear electromagnetic field. The form of local interaction which lead to bounded states of finite masses, charges and spins was constructed. To do this I added Kaluza-Klein Lagrangian on the surface, which is associated with extended particle, to quadratic in field potentials term (a la tachyon mass). This ensures that Lagrangian remains an even function of the field, but spontaneous symmetry breaking leads to nontrivial soliton-like solutions. I assumed that the particle has axial symmetry and that the surface has only one degree of freedom, i.e. is a disk with the radius determined from the equations of motion. The solution of system of two non-linear partial differential equations for the field potentials was obtained numerically by different methods. Several solutions with increasing orders of leading field multipoles and disk radius were obtained, and masses, electric charges and spins were calculated. In the framework of this model the ratio of a charge square to a double spin, i.e. the fine structure constant, which do not depend on parameters of the model, was calculated.