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Published online by Cambridge University Press: 14 October 2002
We consider the inverse connection problem consisting of determining a gauge field on $\mathbb{R}^d$ from its non-abelian Radon transform along oriented straight lines. The determination is considered modulo gauge transformations. Our results include: global uniqueness theorems for $d\geq3$, new local uniqueness theorems for $d=2$, constructive proofs (i.e. proofs containing reconstruction procedures), counterexamples to the global uniqueness for $d=2$, a reduction to the attenuated X-ray transform.
AMS 2000 Mathematics subject classification: Primary 53C65; 81U40