Inverse problem for the Yang-Mills equations

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.

References in corpus (3)

• Identification of nonlinearity in conductivity equation via Dirichlet-to-Neumann map
• Reconstruction for the coefficients of a quasilinear elliptic partial differential equation
• Reconstruction of Lorentzian manifolds from boundary light observation sets

Cited by in corpus (4)

• Stability estimate for the broken non-abelian X-ray transform in Minkowski space
• Inverse problems for non-linear hyperbolic equations with disjoint sources and receivers
• Stability estimates for inverse problems for semi-linear wave equations on Lorentzian manifolds
• Survey on Broken Ray Transforms