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.
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Acknowledgements
GPP and HZ were supported by EPSRC Grant EP/M023842/1. GU was partly supported by NSF, a Si-Yuan Professorship at HKUST and a FiDiPro Professorship of the Academy of Finland. GPP and HZ would like to express their gratitude to the University of Washington at Seattle for hospitality while part of this work was being carried out. We are grateful to Leo Butler for a helpful discussion concerning adjoint orbits and to Alexander Strohmaier for pointing out that Wong’s equations appear as semi-classical limits. Finally, we thank the referee for many valuable comments and corrections.
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Paternain, G.P., Uhlmann, G. & Zhou, H. Lens Rigidity for a Particle in a Yang–Mills Field. Commun. Math. Phys. 366, 681–707 (2019). https://doi.org/10.1007/s00220-019-03388-6
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DOI: https://doi.org/10.1007/s00220-019-03388-6