Temporal discretisation of the Skyrme Model

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.