Inverse Problem for the Yang–Mills Equations

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$${\mathbb {R}}^{1+3}$$. 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.