Screw Photon-Like (3+1)-Solitons in Extended Electrodynamics

TL;DR

This paper constructs explicit spatially finite screw-shaped photon-like soliton solutions in Extended Electrodynamics, linking their properties to quantum concepts like spin and Planck's relation.

Contribution

It introduces a novel class of screw soliton solutions in EED and a new description of spin momentum based on energy-momentum exchange between field components.

Findings

Explicit screw soliton solutions are constructed.

A new spin momentum description within EED is proposed.

The relation between soliton sizes and quantum energy is established.

Abstract

This paper aims to present explicit photon-like (3+1) spatially finite soliton solutions of screw type to the vacuum field equations of Extended Electrodynamics (EED) in relativistic formulation. We begin with emphasizing the need for spatially finite soliton modelling of microobjects. Then we briefly comment the properties of solitons and photons and recall some facts from EED. Making use of the localizing functions from differential topology (used in the partition of unity) we explicitly construct spatially finite screw solutions. Further a new description of the spin momentum inside EED, based on the notion for energy-momentum exchange between $F$ and $*F$, isintroduced and used to compute the integral spin momentum of a screw soliton. The consistency between the spatial and time periodicity naturally leads to a particular relation between the longitudinal and transverse sizes of the screw solution, namely, it is equal to $\pi$. The Planck's formula $E=h\nu$ in the form of $ET=h$ arizes as a measure of the integral spin momentum.