Conjugate linear perturbations of Dirac operators and Majorana fermions

TL;DR

This paper investigates a broad class of perturbations of Dirac operators across dimensions, extending the Jackiw-Rossi model, and analyzes their low energy spectra on complete surfaces.

Contribution

It introduces a generalized class of Dirac operator perturbations applicable in any dimension and provides spectral analysis on complete surfaces.

Findings

Generalized Dirac perturbations applicable in all dimensions

Spectral description of these operators on complete surfaces

Extension of the Jackiw-Rossi model to broader contexts

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.