Semi-localized axial state of a relativistic electron

TL;DR

This paper introduces a novel semi-localized quantum state of a relativistic electron that is self-consistent with its electromagnetic field, characterized by a transverse width equal to the Compton wavelength.

Contribution

It presents the first theoretical description of a semi-localized relativistic electron state that incorporates self-interaction with its electromagnetic field.

Findings

The transverse width of the state equals the electron's Compton wavelength.

The state is self-consistent with electromagnetic interactions.

It describes an electron moving freely along one direction while localized in a plane.

Abstract

The new quantum state of a relativistic electron in a vacuum is described. It corresponds to an electron moving freely along a certain direction and being self-localized in a plane which is transverse to its momentum. This semi-localized state is self-consistent with respect to the interaction of an electron with its own electromagnetic field. The width of a transverse distribution is proved to be the Compton wavelength of an electron