Lens rigidity for a particle in a Yang-Mills field

TL;DR

This paper demonstrates that, under certain conditions, the external Yang-Mills potential influencing a classical particle can be uniquely reconstructed from lens data, including scattering information and travel times, on a compact manifold.

Contribution

It establishes a lens rigidity result for a particle in a Yang-Mills field, showing potential recovery up to gauge transformations from boundary measurements.

Findings

Potential $A$ can be uniquely recovered from lens data.

Recovery is up to gauge transformations.

Results hold under convexity assumptions on the manifold.

Abstract

We consider the motion of a classical colored spinless particle under the influence of an external Yang-Mills potential $A$ on a compact manifold with boundary of dimension $\geq 3$. We show that under suitable convexity assumptions, we can recover the potential $A$, up to gauge transformations, from the lens data of the system, namely, scattering data plus travel times between boundary points.