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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_00011v1  (pdf)
Date submitted: 2024-12-04 19:02
Submitted by: Palmerduca, Eric
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Atomic, Molecular and Optical Physics - Theory
  • High-Energy Physics - Theory
  • Mathematical Physics
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.

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
Current status:
Has been resubmitted

Reports on this Submission

Report #2 by Anonymous (Referee 2) on 2025-1-29 (Invited Report)

Report

Overall, I found the manuscript nicely presented, and easy to follow, and helpful in filling the long-standing knowledge gap, especially in field of optics. However, I do not agree with certain claims and arguments presented in this paper, as highlighted in my report. I strongly believe that the authors' should address these concerns, and incorporate the necessary revisions to the manuscript.

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Recommendation

Ask for major revision

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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

Report #1 by Ivan Fernandez Corbaton (Referee 1) on 2025-1-20 (Invited Report)

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Report

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Requested changes

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Recommendation

Ask for major revision

  • validity: high
  • significance: top
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: excellent

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

Attachment:

SciPost_response_to_Ref_A.pdf

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