The attenuated ray transform for connections and Higgs fields
Differential Geometry
2012-03-14 v2 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We show that for a simple surface with boundary the attenuated ray transform in the presence of a unitary connection and a skew-Hermitian Higgs field is injective modulo the natural obstruction for functions and vector fields. We also show that the connection and the Higgs field are uniquely determined by the scattering relation modulo a gauge transformation. The proofs involve a Pestov type energy identity for connections together with holomorphic gauge transformations which arrange the curvature of the connection to have definite sign.
Cite
@article{arxiv.1108.1118,
title = {The attenuated ray transform for connections and Higgs fields},
author = {Gabriel P. Paternain and Mikko Salo and Gunther Uhlmann},
journal= {arXiv preprint arXiv:1108.1118},
year = {2012}
}
Comments
27 pages, to appear in Geom. Funct. Anal