The parastatistics of braided Majorana fermions

Abstract

This paper presents the parastatistics of braided Majorana fermions obtained in the framework of a graded Hopf algebra endowed with a braided tensor product. The braiding property is encoded in a $t$-dependent $4\times 4$ braiding matrix $B_t$ related to the Alexander-Conway polynomial. The nonvanishing complex parameter t defines the braided parastatistics. At $t=1$ ordinary fermions are recovered. The values of $t$ at roots of unity are organized into levels which specify the maximal number of braided Majorana fermions in a multiparticle sector. Generic values of $t$ and the $t=-1$ root of unity mimick the behaviour of ordinary bosons.

7 pages; contribution to the proceedings of the 34th International Colloquium on Group Theoretical Methods in Physics, Strasbourg, 18-22 July 2022

References in corpus (2)

• Non-Abelian Anyons and Topological Quantum Computation
• First quantization of braided Majorana fermions

Cited by in corpus (2)

• Volichenko-type metasymmetry of braided Majorana qubits
• On braid statistics versus parastatistics