Tomio Umeda
Eigenfunctions of Dirac operators at the threshold energies
(247K, pdf)

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