Charged spinning fermionic configurations and a mass gap

TL;DR

This paper constructs a classical nonlinear spinor field model with electromagnetic coupling that produces finite-energy, particle-like solutions with properties similar to electrons, including a mass gap, charge gap, and spin.

Contribution

It introduces a self-consistent axially symmetric system with nonlinear spinor and Maxwell fields, revealing a mass gap, charge gap, and localized spinning solutions resembling electrons.

Findings

Existence of a mass gap and charge gap due to nonlinearity.

Finite-energy localized solutions with electron-like properties.

Electric charge causes qualitative changes in system behavior.

Abstract

We consider a self-consistent axially symmetric system supported by a classical nonlinear spinor field minimally coupled to electric and magnetic Maxwell fields. The presence of the nonlinearity of the spinor field ensures the existence of a minimum positive energy of the system (a mass gap), of a minimum charge (a charge gap), and of a minimum magnetic moment. In turn, the presence of the electric charge results in qualitative changes in the behavior of physical characteristics of the systems under consideration as compared with the case of an electrically neutral spinor field. It is shown that, with a suitable choice of free system parameters, there exists a regular finite-energy particlelike solution describing a localized spinning object whose physical parameters correspond to the main characteristics of an electron/positron (including the spin equal to $1/2$), but with the characteristic size comparable to the corresponding Compton wavelength. Also, we show that four local Dirac equations are equivalent to two nonlocal equations.