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The attenuated ray transform for connections and Higgs fields. (English) Zbl 1256.53021

Summary: 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.

MSC:

53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
81T13 Yang-Mills and other gauge theories in quantum field theory
53C22 Geodesics in global differential geometry
37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
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