On the range of the attenuated magnetic ray transform for connections and Higgs fields

Abstract

For a two-dimensional simple magnetic system, we study the attenuated magnetic ray transform $I_{A,\Phi }$, with attenuation given by a unitary connection $A$ and a skew-Hermitian Higgs field $\Phi$. We give a description for the range of $I_{A,\Phi }$ acting on ${\mathbb{C}}^n$-valued tensor fields.

arXiv comment21 pages; Introduction section is restructured, Section 4 has been completely rewritten, and some other revisions were made