- 08-100 Tomio Umeda
- Eigenfunctions of Dirac operators at the threshold energies
(247K, pdf)
May 29, 08
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Abstract. We show that the eigenspaces of
the Dirac operator $H=\alpha\cdot ( D - A(x) ) + m \beta $ at
the threshold energies $\pm m$ are
coincide with the direct sum of the zero space and the kernel of
the Weyl-Dirac operator $\sigma\cdot ( D - A(x) )$.
Based on this result, we describe the asymptotic limits of
the eigenfunctions of the Dirac operator corresponding to
these threshold energies. Also, we discuss the set of vector
potentials for which the kernels of $H\mp m$ are non-trivial,
i.e. $\mbox{Ker}(H\mp m) \not = \{ 0 \}$.
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