Majorana Fermions and Representations of the Braid Group

摘要

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