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Four no-go theorems on the existence of spin and orbital angular momentum of massless bosons
by Eric Palmerduca, Hong Qin
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Submission summary
| Authors (as registered SciPost users): | Eric Palmerduca |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202412_00011v2 (pdf) |
| Date submitted: | Feb. 27, 2025, 11:14 p.m. |
| Submitted by: | Palmerduca, Eric |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
The past decades have seen substantial interest in the so-called orbital angular momentum (OAM) of light, driven largely by its diverse range of applications. However, there are fundamental theoretical issues with decomposing the angular momentum of massless particles, such as photons, into spin (SAM) and orbital angular momentum parts. While the angular momentum of massive particles has a natural splitting into the Wigner SAM and OAM, there are numerous proposed splittings for photons and no consensus about which is correct. Moreover, it has been shown that most of the proposed SAM and OAM operators do not satisfy the defining commutation relations of angular momentum operators and are thus not legitimate splittings. Here, we prove that it is generally impossible to split the total angular momentum operator of massless bosons, such as photons and gravitons, into spin and orbital parts. We prove two further generalizations of this result, showing that there are no SAM-OAM splittings even if (1) the SAM operator generates non-internal symmetries or (2) if one allows the SAM and OAM operators to generate non-SO(3) symmetries.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
Current status:
Reports on this Submission
Report #3 by Anonymous (Referee 3) on 2025-4-9 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202412_00011v2, delivered 2025-04-09, doi: 10.21468/SciPost.Report.10987
Report
\begin{equation}
[J_a,J_b]=i\epsilon_{abc}J_c.
\end{equation}
The authors have further explored generalized scenarios involving non-internal symmetry implementations for spin operators and non-$SO(3)$ symmetry extensions for both spin and orbital angular momentum operators. Through these extensions, they consistently arrive at the central conclusion that such decomposition remains fundamentally unattainable. The study's original motivation rooted in experimental optics contexts is valuable, offering insights into angular momentum decomposition challenges within specific physical implementations.
While the conclusion is physically sound, the analysis could be significantly strengthened by addressing the unique
$ISO(2)$ little group structure to massless particles. Specifically, the critical distinction between helicity operators ($h$) and spin angular momentum operators ($\bm S$) warrants deeper consideration. A potentially fruitful modification might involve redefining the commutation relations in (15)-(16) as:
\begin{equation}
[J_a,h]=\cdots,\quad [h,h]=0
\end{equation} while relaxing constraints on orbital angular momentum. This proposed refinement does not diminish the current work's significance, but rather complements it by addressing the fundamental differences between massive and massless particle representations.
Recommendation
Ask for minor revision
Report #2 by Ivan Fernandez Corbaton (Referee 1) on 2025-3-18 (Invited Report)
Report
After the last responses from the authors, I can now recommend the publication of the article.
Best regards
Ivan Fernandez-Corbaton
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
Report #1 by Ivan Fernandez Corbaton (Referee 1) on 2025-3-4 (Invited Report)
- Cite as: Ivan Fernandez Corbaton, Report on arXiv:scipost_202412_00011v2, delivered 2025-03-04, doi: 10.21468/SciPost.Report.10770
Strengths
Weaknesses
Report
Requested changes
Please see the attached file: palmerduca_second.pdf
Recommendation
Ask for minor revision
Author: Eric Palmerduca on 2025-03-17 [id 5295]
(in reply to Report 1 by Ivan Fernandez Corbaton on 2025-03-04)We sincerely thank the Referee for their additional comments and have addressed each in the attached document.
Author: Eric Palmerduca on 2025-04-16 [id 5378]
(in reply to Report 3 on 2025-04-09)We greatly appreciate the Referee's feedback; our response in the attached document.
Attachment:
Response_to_Report_3_on_scipost_202412_00011v2.pdf