Heriot-Watt Mathematics Report Series
HWM02-59, 3 December 2003
The Local Structure of Zero Mode Producing Magnetic Potentials
D M Elton
Abstract
We consider the class of continuous magnetic potentials on $R^3$ 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 $m\ge3$.
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