The attenuated ray transform for connections and Higgs fields

Details The attenuated ray transform for connections and Higgs fields The attenuated ray transform for connections and Higgs fields

2011-08-04

arxiv.org/abs/1108.1118v2

Mathematics

Differential Geometry

27 pages, to appear in Geom. Funct. Anal

Scientific paper

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.

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