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.
Highlights
This paper considers a nonlinear geometric inverse problem associated with the motion of a classical colored spinless particle under the influence of an external Yang–Mills potential A
In order to set up the inverse problem, let us give first a brief description of the system in question and the physical background
Since G is compact we can fix once and for all a bi-invariant metric on G, or equivalently, we endow g with an Ad-invariant metric ·, · ; with this metric we identify g∗ with g
Summary
This paper considers a nonlinear geometric inverse problem associated with the motion of a classical colored spinless particle under the influence of an external Yang–Mills potential A. A predecessor to Theorem 1.2 appears in [30] for the abelian case G = U (1) Another application of the scheme above are the results in [13] in which the problem of recovering a connection from parallel transport along geodesics is considered, but in this case, the underlying dynamical system (the geodesic flow) is unaffected by the external field. For this we need to assume that we know i∗ A and that O contains a basis of g.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
