Inverse Problem for the Yang–Mills Equations

Xi Chen, Matti Lassas, Lauri Oksanen, Gabriel P. Paternain

OAI: oai:www.repository.cam.ac.uk:1810/322663 • DOI: 10.17863/CAM.70119

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.

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