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Inverse Problem for the Yang–Mills Equations

Chen, X; Lassas, M; Oksanen, L; Paternain, GP; (2021) Inverse Problem for the Yang–Mills Equations. Communications in Mathematical Physics , 384 pp. 1187-1225. 10.1007/s00220-021-04006-0. Green open access

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Abstract

We show that a connection can be recovered up to gauge from source-to-solution type data associated with the Yang–Mills equations in Minkowski space R1+3. Our proof analyzes the principal symbols of waves generated by suitable nonlinear interactions and reduces the inversion to a broken non-abelian light ray transform. The principal symbol analysis of the interaction is based on a delicate calculation that involves the structure of the Lie algebra under consideration and the final result holds for any compact Lie group.

Type: Article
Title: Inverse Problem for the Yang–Mills Equations
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s00220-021-04006-0
Publisher version: http://dx.doi.org/10.1007/s00220-021-04006-0
Language: English
Additional information: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI: https://discovery.ucl.ac.uk/id/eprint/10127344
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