Conjugate linear perturbations of Dirac operators and Majorana fermions

Abstract

We study a canonical class of perturbations of Dirac operators that are defined in any dimension and on any Hermitian Clifford module bundle. These operators generalize the 2-dimensional Jackiw-Rossi operator, which describes electronic excitations on topological superconductors. We also describe the low energy spectrum of these operators on complete surfaces, under mild hypotheses.

31 pages, no figures. Accepted in The Journal of Geometric Analysis. Comments are still welcome!