Non-Commutative Scalar Fields

In this paper, we explore numerical methods for simulating scalar field configurations in non-commutative two-dimensional spaces. We focus on the finite difference techniques employed to compute mixed partial derivatives and the action functional in the presence of non-commutative corrections. The methods presented address the challenges posed by non-commutative geometry, specifically in computing the mixed derivative terms that arise due to the deformation of spatial coordinates. We introduce semi-implicit time-stepping schemes to ensure numerical stability when dealing with stiff nonlinear terms. The approaches discussed here provide a framework for simulating and analyzing physical systems influenced by non-commutativity, which are not extensively documented in existing literature.