  We show that a connection can be recovered up to gauge from
source-to-solution type data associated with the Yang-Mills equations in the
four dimensional Minkowski space. 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.
