Statistics of Abelian topological excitations

Abstract

In this paper, we develop a novel theory that generalizes the concept of anyon statistics to Abelian topological excitations of any dimension. We axiomatize excitations as a selected collection of states and operators satisfying the configuration axiom and the locality axiom, purely based on many-body quantum mechanics. Upon these axioms, we define a rigorous and self-contained theory of statistics using only basic algebra and can be implemented on a computer. While our theory is developed independently, the results align with existing physical theories.