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

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.

## 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.