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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 | |
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| Preprint Link: | scipost_202212_00031v1 (pdf) |
| Date submitted: | Dec. 16, 2022, 9:49 a.m. |
| Submitted by: | Seiichi Kuwata |
| 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
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
Author: Seiichi Kuwata on 2023-01-10 [id 3223]
(in reply to Report 1 on 2023-01-05)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.