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The parastatistics of braided Majorana fermions

by Francesco Toppan

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Submission summary

Authors (as registered SciPost users): Francesco Toppan
Submission information
Preprint Link: scipost_202212_00044v2  (pdf)
Date accepted: 2023-08-11
Date submitted: 2023-02-16 01:40
Submitted by: Toppan, Francesco
Submitted to: SciPost Physics Proceedings
Proceedings issue: 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022)
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Mathematical Physics
Approach: Theoretical


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.

Published as SciPost Phys. Proc. 14, 046 (2023)

Author comments upon resubmission

Dear Editors,

following your request of a minor revision I have inserted a paragraph
explaining why the Z_2-graded qubits describe Majorana fermions.
Two extra references ([10] and [11]) have been added with respect
to the previous version.

Sincerely Yours,

Francesco Toppan

List of changes

A paragraph (4 lines) has been added after formula (3) at page 2:

from “The excited state is a Majorana …”
till “ … (implying that the charge conjugation operator is the identity).”

Two extra references ([10] and [11]) have been added.

Submission & Refereeing History

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Resubmission scipost_202212_00044v2 on 16 February 2023

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