Temporal discretisation of the Skyrme Model

TL;DR

This paper discusses a principled approach to discretising the Skyrme model for real-time simulations, aiming to preserve invariants of motion and improve numerical accuracy in soliton-based nuclear physics models.

Contribution

It introduces a novel discretisation method that maintains exact invariants in the Skyrme model, enhancing the reliability of real-time soliton simulations.

Findings

Developed principles for discretising soliton models

Constructed exact discrete invariants for the Skyrme model

Improved numerical stability in real-time simulations

Abstract

Soliton models are used in elementary particle physics and nuclear physics to model extended objects such as nucleons, using effective field theories derived from more fundamental theories such as QCD. Computer simulation requires some sort of discretisation procedure, a notable example being lattice gauge theory applied in the imaginary time formulation. In this lecture we focus on simulation in real time and the problems which arise when invariants of the motion are monitored in a simulation. Ad hoc discretisations invariably introduce drift in numerically computed invariants, due not only to numerical accuracy (which can be negligible), but with the fact that the discretisation may not necessarily imply conservation. We discuss an approach developed which gives principles for the discretisation of such systems and for the construction of exact discrete invariants of the motion. This approach is applied to the Skyrme model. Talk at the International Workshop on Nuclear Theory, Rila, June 2001, to be published in the Proceedings.