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On the spin content of the classical massless Rarita--Schwinger system
by Mauricio Valenzuela and Jorge Zanelli
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Submission summary
| Authors (as registered SciPost users): | Mauricio Valenzuela |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202211_00048v1 (pdf) |
| Date submitted: | 2022-11-24 23:00 |
| Submitted by: | Valenzuela, Mauricio |
| 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
We analyze the Rarita--Schwinger massless theory in the Lagrangian and Hamiltonian approaches. At the Lagrangian level, the standard gamma-trace gauge fixing constraint leaves a spin-1/2 and a spin-3/2 propagating Poincare group helicities. At the Hamiltonian level, the result depends on whether the Dirac conjecture is assumed or not. In the affirmative case, a secondary first class constraint is added to the total Hamiltonian and a corresponding gauge fixing condition must be imposed, completely removing the spin-1/2 sector. In the opposite case, the spin-1/2 field propagates and the Hamilton field equations match the Euler-Lagrange equations.
Current status:
Reports on this Submission
Report #1 by Jean-Pierre Gazeau (Referee 1) on 2023-1-11 (Invited Report)
- Cite as: Jean-Pierre Gazeau, Report on arXiv:scipost_202211_00048v1, delivered 2023-01-11, doi: 10.21468/SciPost.Report.6505
Strengths
1) In their submitted paper, the authors revisit the Dirac conjecture as which a \textit{all first class constraints are gauge generators} by presenting a careful analysis of the massless Rarita-Schwinger equations for 3/2 spin field.
2) They compare Lagrangian and Hamiltonian approaches to the question. Interestingly they prove that both approaches are consistent. Furthermore they match under the condition that the Dirac conjecture is ignored.
Weaknesses
Let me suggest that the authors also consider the appearance of undecomposable representations of the Poincar\'e group in the massless case, and the subsequent Gupta-Bleuler structures in which gauge fields are ignored if one works with cosets in Hilbert space of states (see for instance W. Heidenreich, On solution spaces of massless field equations with arbitrary spin, \textit{J. Math. Phys.} \textbf{27}, 2154 (1986).
Report
This Journal's acceptance criteria are met
Requested changes
A few text corrections should be considered by the authors.
\begin{enumerate}
\item Line above Equation (7): ``is represents'' ?
\item Symbol $D$ is introduced in Equation (7) without giving its meaning.
\item Line 7 below Eq. (8) : ``constraints" and not ``constraint''.
\item In first paragraph of Section 2, ``kernel" and not ``Kernel".
\end{enumerate}
Author: Mauricio Valenzuela on 2023-01-23 [id 3261]
(in reply to Report 1 by Jean-Pierre Gazeau on 2023-01-11)Dear Editor:
We thank the referee for the valuable comments and the suggested reference by Heidenreich. We did not know the article of Heidenreich and we think helps with the quantization problem of the system, which we should handle in the next future. Accordingly, we added a paragraph in the Conclusions section, page 7, which reads
"As for quantization issues, the \tralf sector of the massless RS field has been quantized in various approaches \cite{Senjanovic:1977vr,Pilati:1977ht,Fradkin:1977wv,Heidenreich:1986vx}. In all of them, both \half sectors of the Poincar\'e group decomposition are factored out. Following reference \cite{Heidenreich:1986vx}---where it is shown that the massless RS field decomposes in a \half (pure gauge) sector with 0-norm, and \half and \tralf sectors of positive norm---the massless RS can be quantized \`a la Gupta-Bleuler factoring out only the zero norm state."
We hope that with this modification the paper will fulfill the referee requirements.
Sincerely,
the authors.