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Spin degrees of freedom incorporated in conformal group: Introduction of an intrinsic momentum operator

by S. Kuwata

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Submission summary

Authors (as registered SciPost users): Seiichi Kuwata
Submission information
Preprint Link: scipost_202212_00031v1  (pdf)
Date submitted: 2022-12-16 09:49
Submitted by: Kuwata, Seiichi
Submitted to: SciPost Physics Proceedings
Proceedings issue: 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022)
Ontological classification
Academic field: Physics
Specialties:
  • Mathematical Physics
Approach: Theoretical

Abstract

Considering spin degrees of freedom incorporated in the conformal group, we introduce an intrinsic momentum operator $\pi_\mu$, which is feasible for the Bhabha wave equation. If a physical state $\psi_{\rm ph}$ for spin $s$ is annihilated by the $\pi_\mu$, the degree of $\psi_{\rm ph}$, ${\rm deg} \, \psi_{\rm ph}$, should equal twice the spin degrees of freedom, $2 ( 2 s + 1)$, where the muptiplicity $2$ indicates the chirality. The relation ${\rm deg} \, \psi_{\rm ph} = 2 ( 2 s + 1)$ holds in the representation ${\rm R}_5 (s,s)$, irreducible representation of the Lorentz group in five dimensions.

Current status:
Has been resubmitted

Reports on this Submission

Report #1 by Anonymous (Referee 1) on 2023-1-5 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202212_00031v1, delivered 2023-01-05, doi: 10.21468/SciPost.Report.6443

Report

See the uploaded file.

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  • validity: ok
  • significance: ok
  • originality: high
  • clarity: low
  • formatting: good
  • grammar: reasonable

Author:  Seiichi Kuwata  on 2023-01-10  [id 3223]

(in reply to Report 1 on 2023-01-05)
Category:
answer to question
correction

The referee writes:
"It should be clarified which equation, massive or massless, is considered."

Our response:
We consider a massive wave equation, where a spin degrees of freedom is given by (2s+1).

The referee writes:
"there is a possibility that a physical state will not annihilated by the intrinsic momentum operator."

Our response:
We clarify the two types of intrinsic momentum operators by distinguishing the chirality. Each of the intrinsic momentum operators annihilates a physical state of the corresponding chirality.

The referee writes:
"There are some sentences with unclear meanings and typos."

Our response:
Some typos are corrected, and on p.6, 2nd line after eq.(24), we give a supplementary explanation of the example.

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