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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:  20230811 
Date submitted:  20230110 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 
Specialties: 

Approach:  Theoretical 
Abstract
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.
Author comments upon resubmission
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.
Published as SciPost Phys. Proc. 14, 034 (2023)
Reports on this Submission
Strengths
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
Weaknesses
There are no weakness
Report
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.