The local structure of the set of zero mode producing magnetic potentials.

Elton, Daniel M. (2002) The local structure of the set of zero mode producing magnetic potentials. Communications in Mathematical Physics, 229 (1). pp. 121-139. ISSN 0010-3616

Abstract

We consider the class of continuous magnetic potentials on ℝ3 which decay as o(|x|− 1). Within this class it is shown that the set of potentials whose associated Weyl-Dirac operator produces zero modes with multiplicity m forms a smooth submanifold of co-dimension m 2 when m= 0, 1, 2, and is contained in a smooth submanifold of co-dimension 2m− 1 when m≥ 3.