The parastatistics of braided Majorana fermions

• URL: http://arxiv.org/abs/2312.06693v1
• Date: Sat, 9 Dec 2023 15:17:01 GMT
• Title: The parastatistics of braided Majorana fermions
• Authors: Francesco Toppan
• Abstract summary: The braided Majorana fermions are obtained in a graded Hopf algebra endowed with a braided tensor product. The values of $t$ at roots of unity are organized into levels which specify the number of braided Majorana fermions in a multiparticle sector.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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