Simulating the scalar field using the fuzzy sphere

摘要

Fuzzy spaces provide a new approximation scheme using (non-commutative) matrix algebras to approximate the algebra of function of the continuous space. This paper describes how to implement a numerical scheme based on a fuzzy space approximation. In this first attempt, the simplest fuzzy space and field theory, respectively the fuzzy two-sphere and the real scalar field, are used to simulate the real scalar field on the plane. Along the way, this method is compared to its traditional lattice discretisation equivalent. [References: 15]