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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_00044v1 (pdf) |
| Date submitted: | 2022-12-18 10:58 |
| 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.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2022-12-28 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202212_00044v1, delivered 2022-12-28, doi: 10.21468/SciPost.Report.6401
Weaknesses
Unclear if this has any physics applications. Much is repeated from earlier work by same author.
Report
I have read "The parastatistics of braided Majorana fermions" by
Francesco Toppan. Toppan has constructed a representation of the
braid group based on the burau representation. One can debate the
meaning of this result (and whether or not the use of the word
"Majorana" is actually appropriate here). I will not argue these
points. My main complaint about this work is simply that it is not
going to be of much interest to most of the readers of SciPost. To
start with, much of the work is just a summary of an earlier work (Nuc
Phys B 980) by the same author and very little further is new.
Secondly, there is no attempt to identify any reasonable physical
system that this mathematics applies to. I therefore do not think
this work is publishable in SciPost, but rather should be submitted to
a specialist journal.
Author: Francesco Toppan on 2023-02-06 [id 3314]
(in reply to Report 1 on 2022-12-28)Since the SciPost web interface does not allow me to submit the revision requested by the Editor
I use this window to attach the pdf file of my revision where I point out why the fermions considered
in the paper are Majorana's.
Attachment:
gr34toppanrevised.pdf