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Eigenfunctions of Dirac operators at the threshold energies

Authors
  • Umeda, Tomio
Type
Preprint
Publication Date
May 27, 2008
Submission Date
May 27, 2008
Source
arXiv
License
Yellow
External links

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. ${Ker}(H\mp m) \not = \{0 \}$.

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