Implicit schemes for real-time lattice gauge theory

TL;DR

This paper introduces gauge-covariant implicit numerical schemes for real-time lattice gauge theory, improving stability and accuracy in simulations of classical Yang-Mills fields relevant to heavy-ion collisions.

Contribution

It presents a novel semi-implicit scheme that addresses numerical instability and dispersion issues in 3D Yang-Mills simulations, ensuring gauge covariance and Gauss constraint conservation.

Findings

The semi-implicit scheme stabilizes 3D Yang-Mills simulations.

Wave propagation is accurately modeled along one lattice direction.

The scheme maintains gauge covariance and Gauss constraint conservation.

Abstract

We develop new gauge-covariant implicit numerical schemes for classical real-time lattice gauge theory. A new semi-implicit scheme is used to cure a numerical instability encountered in three-dimensional classical Yang-Mills simulations of heavy-ion collisions by allowing for wave propagation along one lattice direction free of numerical dispersion. We show that the scheme is gauge covariant and that the Gauss constraint is conserved even for large time steps.