- 09-190 Yoshimi Saito, Tomio Umeda
- Eigenfunctions at the threshold energies of magnetic Dirac operators
(193K, LaTeX2e )
Oct 15, 09
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Abstract. We propose a simple proof of characterization of the eigenspaces
corresponding to the eigenvalues $\pm m$ of a supersymmetric Dirac operator $H=Q + m\tau$, where $Q$ is a supercharge, $m$ a positive constant, and $\tau$ the unitary involution. The proof is abstract, but not relevant to the abstract Foldy-Wouthuysen transformation. We then apply the obtained results to magnetic Dirac operators, and derive a series of new results on the magnetic Dirac operators, such as the asymptotic behaviors at infinity of the $\pm m$ modes, and sparseness of vector potentials which give rise to the $\pm m$ modes.