This article is concerned with the analysis of Dirac operators D twisted by ramified Euclidean line bundles (Z, l) -motivated by their relation with harmonic Z/2Z spinors, which have appeared in various context in gauge theory and calibrated geometry. The closed extensions of D are described in terms of the Gelfand-Robbin quotient H. Assuming that the branching locus Z is a closed cooriented codimension two submanifold, a geometric realisation of H is constructed. This, in turn, leads to an L² regularity theory.
Bera et al. (Mon,) studied this question.