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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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Authors (as registered SciPost users): | Eric Palmerduca |
Submission information | |
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Preprint Link: | scipost_202412_00011v1 (pdf) |
Date submitted: | Dec. 4, 2024, 7:02 p.m. |
Submitted by: | Palmerduca, Eric |
Submitted to: | SciPost Physics |
Ontological classification | |
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Academic field: | Physics |
Specialties: |
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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 such an SAM-OAM splitting is unambiguous for massive particles, 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.
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Report #2 by Anonymous (Referee 2) on 2025-1-29 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202412_00011v1, delivered 2025-01-29, doi: 10.21468/SciPost.Report.10572
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Report #1 by Ivan Fernandez Corbaton (Referee 1) on 2025-1-20 (Invited Report)
- Cite as: Ivan Fernandez Corbaton, Report on arXiv:scipost_202412_00011v1, delivered 2025-01-20, doi: 10.21468/SciPost.Report.10521
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Author: Eric Palmerduca on 2025-02-27 [id 5248]
(in reply to Report 1 by Ivan Fernandez Corbaton on 2025-01-20)See attached for a detailed response to each comment
Author: Eric Palmerduca on 2025-02-27 [id 5249]
(in reply to Report 2 on 2025-01-29)See attached for a detailed response to each comment
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SciPost_response_to_Ref_B.pdf