# Quantum diffusion of electromagnetic fields of ultrarelativistic spin-half particles

## TL;DR

This paper investigates the quantum diffusion effects on electromagnetic fields generated by ultrarelativistic spin-half particles, revealing deviations from classical Coulomb fields at microscopic distances.

## Contribution

It introduces a quantum wave packet approach to compute electromagnetic fields, highlighting the diffusion effect for relativistic particles described by the Dirac equation.

## Key findings

- Electromagnetic fields differ from Coulomb fields at the Compton wavelength scale.
- Quantum diffusion causes the electromagnetic field to spread out more than classical predictions.
- Results provide insights into quantum effects in high-energy particle fields.

## Abstract

We compute electromagnetic fields created by a relativistic charged spin-half particle in empty space at distances comparable to the particle Compton wavelength. The particle is described as a wave packet evolving according to the Dirac equation. It produces the electromagnetic field that is essentially different from the Coulomb field due to the quantum diffusion effect.