Spinor pairs and the concentration principle for Dirac operators

Abstract

We study perturbed Dirac operators of the form Ds = D + sA : Γ(E) → Γ(F ) over a compact Riemannian manifold (X, g) with symbol c and special bundle maps A : E → F for s >> 0. Under a simple algebraic criterion on the pair (c, A), solutions of Dsψ = 0 concentrate as s → ∞ around the singular set ZA ⊂ X of A. We give many examples, the most interesting ones arising from a general "spinor pair" construction.

Conjugate linear perturbations of Dirac operators and Majorana fermions

“…The key analytic observation in studying the Jackiw-Rossi equation is that the planar Jackiw-Rossi operator comes from a concentrating pair, in the sense of Maridakis; cf. [15,Definition 2.1]. In other words, the operator…”