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The parastatistics of braided Majorana fermions
by Francesco Toppan
This Submission thread is now published as
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 |
| Specialties: |
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| Approach: | Theoretical |
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.
Author comments upon resubmission
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.
Published as SciPost Phys. Proc. 14, 046 (2023)