Majorana Fermions and Representations of the Braid Group

TL;DR

This paper explores how Majorana Fermions relate to braid group representations, revealing new algebraic structures and generalizing previous findings in the context of Clifford algebras and braiding.

Contribution

It provides a general proof connecting Clifford algebra-based Majorana operators to braid group representations, extending prior work on Ivanov braiding and extraspecial 2-groups.

Findings

Majorana operators generate extraspecial 2-groups.

Braid group representations can be derived from Majorana operator strings.

The results unify and extend previous algebraic observations in the field.

Abstract

In this paper we study unitary braid group representations associated with Majorana Fermions. Majorana Fermions are represented by Majorana operators, elements of a Clifford algebra. The paper recalls and proves a general result about braid group representations associated with Clifford algebras, and compares this result with the Ivanov braiding associated with Majorana operators. The paper generalizes observations of Kauffman and Lomonaco and of Mo-Lin Ge to show that certain strings of Majorana operators give rise to extraspecial 2-groups and to braiding representations of the Ivanov type.