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SO(1,3) Yang-Mills solutions on Minkowski space via cosets

by Kaushlendra Kumar

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Submission summary

Authors (as registered SciPost users): Kaushlendra Kumar
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-08-11
Date submitted: 2022-12-05 09:04
Submitted by: Kumar, Kaushlendra
Submitted to: SciPost Physics Proceedings
Proceedings issue: 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022)
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


We present a novel family of Yang-Mills solutions, with gauge group SO(1,3), on Minkowski space that are geometrically distinguished into two classes, viz. interior and exterior of the lightcone. We achieve this by foliating the former with SO(1,3)/SO(3) cosets and the latter with SO(1,3)/SO(1,2) cosets and analytically solving the Yang-Mills equation of an SO(1,3)-invariant gauge field. The resulting fields and their stress-energy tensor, when translated to the Minkowski space, diverge at the lightcone, but we demonstrate how this stress-energy tensor could be regularised due to its unique algebraic structure.

Published as SciPost Phys. Proc. 14, 033 (2023)

Submission & Refereeing History

Reports on this Submission

Anonymous Report 1 on 2023-1-5 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2212.01341v1, delivered 2023-01-05, doi: 10.21468/SciPost.Report.6457


This article is based on a report at the 34th International Colloquium on Group Theoretical Methods in Physics. The author considers the method of constructing analytic solutions of the Yang-Mills equations on the Minkowski space by pulling them back from more easily obtained solutions on the spaces R\times SO(1,3)/H with H=SO(3) or SO(1,2). The technique for constructing such solutions is well known for a long time, the author provides relevant references to the literature and applies the methods developed earlier to the case of non-compact gauge groups used in emergent/modified theories of gravity. The article is written in clear language with all the necessary details. All new solutions are derived carefully and explained in detail. I recommend this article for publication in SciPost Physics Proceedings.

Requested changes

Remarks: I think in Conclusion the author means SO(1,3)/H, not SO(3)/H.

  • validity: -
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Author:  Kaushlendra Kumar  on 2023-01-05  [id 3211]

(in reply to Report 1 on 2023-01-05)

Dear Referee,

Thank you for your valuable comments. I agree with you that this typo incurred in the conclusion and it should be rectified in the published version.

Best regards
Kaushlendra Kumar

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