Statistics of Abelian topological excitations

TL;DR

This paper introduces a new, axiomatic theory for Abelian topological excitations of any dimension, generalizing anyon statistics within a rigorous, algebraic framework based on many-body quantum mechanics.

Contribution

It develops a self-contained, algebraic axiomatization of Abelian topological excitations, extending the concept of anyon statistics to higher dimensions and enabling computational implementation.

Findings

The theory aligns with existing physical models.

It provides a rigorous, axiomatic foundation for topological excitations.

The framework is implementable on a computer.

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.