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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_00031v2  (pdf)
Date accepted: 2023-08-11
Date submitted: 2023-01-10 02:12
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
  • Mathematical Physics
Approach: Theoretical


Considering spin degrees of freedom incorporated in the conformal generators, 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, $2 ( 2 s + 1)$ for a massive particle, where the multiplicity $2$ 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.

Published as SciPost Phys. Proc. 14, 034 (2023)

Author comments upon resubmission

Thank you for your valuable comments.

We clarify a wave eqution and the physical state to be presented in this paper.

I hope that the manuscript could be reviewed for considered for publication in SciPost Phys. Proc.

List of changes

(1) The wave equation is restricted to a massive particle, where the spin degrees of freedom is given by (2s+1).

(2) A physical state is distinguished by the chirality.

(3) A supplementary explanation of the Y's after eq.(24) is given.

(4) Some typos are corrected.

Submission & Refereeing History

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Resubmission scipost_202212_00031v2 on 10 January 2023

Reports on this Submission

Anonymous Report 1 on 2023-1-11 (Invited Report)


1) the work shed a light on the problem which usually not considered or neglected.
2) explicit formulae of intrinsic momentum operator are given for some values of spin


There are no weakness


The author has made necessary corrections so that the ponts of the manuscritp are clarified. The issue discussed in this work is an interesting problem and the results are new and will show a way to new insight into conformal symmetry. Thus, it is recommened to accept the present version for publication.

Requested changes

No changes are required.

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

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