# Alternative gauge for the description of the light-matter interaction in a relativistic framework

## TL;DR

This paper introduces a generalized velocity gauge for relativistic light-matter interaction that improves numerical convergence and multipole expansion accuracy, demonstrated through simulations of hydrogen under intense ultrashort laser pulses.

## Contribution

A new velocity gauge formulation for relativistic laser-matter interaction that enhances numerical and multipole expansion convergence compared to traditional minimal coupling.

## Key findings

- Superior convergence in numerical solutions of the Dirac equation.
- Improved accuracy in multipole expansion of laser fields.
- Effective modeling of hydrogen dynamics under intense ultrashort pulses.

## Abstract

We present a generalized velocity gauge form of the relativistic laser-matter interaction. In comparison with the (equivalent) regular minimal coupling description, this new form of the light-matter interaction results in superior convergence properties for the numerical solution of the time-dependent Dirac equation. This applies both to the numerical treatment and, more importantly, to the multipole expansion of the laser field. The advantages of the alternative gauge is demonstrated in hydrogen by studies of the dynamics following the impact of superintense laser pulses of extreme ultraviolet wavelengths and sub-femtosecond duration.