Inverse problem for the Yang-Mills equations
Analysis of PDEs
2021-03-31 v1
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 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.
Cite
@article{arxiv.2005.12578,
title = {Inverse problem for the Yang-Mills equations},
author = {Xi Chen and Matti Lassas and Lauri Oksanen and Gabriel P. Paternain},
journal= {arXiv preprint arXiv:2005.12578},
year = {2021}
}