TY - JOUR

T1 - Majorana Fermions and representations of the braid group

AU - Kauffman, Louis H.

N1 - Publisher Copyright: © 2018 The Author(s).

PY - 2018/8/20

Y1 - 2018/8/20

N2 - 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.

AB - 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.

KW - braid group

KW - braids

KW - extraspecial 2-group

KW - Fermion

KW - Kitaev chain

KW - Knots

KW - links

KW - Majorana Fermion

KW - Majorana string

KW - quantum computing

KW - quantum process

KW - Yang-Baxter equation

KW - ENTANGLEMENT

KW - QUANTUM KNOTS

KW - OPERATORS

UR - http://www.scopus.com/inward/record.url?scp=85051961145&partnerID=8YFLogxK

U2 - 10.1142/S0217751X18300235

DO - 10.1142/S0217751X18300235

M3 - Article

AN - SCOPUS:85051961145

VL - 33

JO - International Journal of Modern Physics A

JF - International Journal of Modern Physics A

SN - 0217-751X

IS - 23

M1 - 1830023

ER -