On the Class of Possible Nonlocal Anyon-Like Operators and Quantum Groups

TL;DR

This paper introduces a new class of nonlocal operators that generate q-deformed algebras, encompassing lattice anyonic operators, and explores their connection to quantum groups.

Contribution

It identifies a broad class of nonlocal operators constructed via disorder operators that produce q-deformed algebras, including known anyonic operators.

Findings

The class includes lattice anyonic operators.

These operators can generate q-deformed algebras.

The approach follows the Schwinger method.

Abstract

We find a class of nonlocal operators constructed by attaching a disorder operator to fermionic degrees of freedom, which can be used to generate q-deformed algebras following the Schwinger approach. This class includes the recently proposed anyonic operators defined on a lattice.