Uhlmann, GuntherGrebnev, Haim2024-09-092024-09-092024-09-092024Grebnev_washington_0250E_26815.pdfhttps://hdl.handle.net/1773/52107Thesis (Ph.D.)--University of Washington, 2024We formulate and prove a gauge equivalence for unitary connections and skew-Hermitian Higgs fields of suitable regularity that are mapped to the same function under the non-abelian X-ray transform on nontrapping asymptotically hyperbolic spaces with negative curvature and no nontrivial twisted conformal Killing tensor fields with certain regularity. If one furthermore fixes such a connection with zero curvature, a corollary provides an injectivity result for the non-abelian X-ray transform over skew-Hermitian Higgs fields.application/pdfen-USCC BY-NC-NDAsymptotically hyperbolic spacesNon-Abelian X-ray transformTransport equationTwisted conformal Killing tensor fieldsMathematicsMedical imagingPhysicsMathematicsThesis