The asymptotic limits of zero modes of massless Dirac operators

Abstract

Asymptotic behaviors of zero modes of the massless Dirac operator $H=\alpha \cdot D+Q(x)$ are discussed, where $\alpha =({\alpha }_1,{\alpha }_2,{\alpha }_3)$ is the triple of $4\times 4$ Dirac matrices, $D=\frac{1}{i}{\nabla }_x$, and $Q(x)=(q_{jk}(x))$ is a $4\times 4$ Hermitian matrix-valued function with $|q_{jk}(x)|\le C<x{>}^{-\rho }$, $\rho >1$. We shall show that for every zero mode $f$, the asymptotic limit of $|x{|}^{2}f(x)$ as $|x|\to +\infty$ exists. The limit is expressed in terms of an integral of $Q(x)f(x)$.

9 pages

References in corpus (6)

• The kernel of Dirac operators on ${\S }^3$ and ${\mathbb{R}}^3$
• Zero modes of the Dirac operator in three dimensions
• Multiple zero modes of the Dirac operator in three dimensions
• Degeneracy of zero modes of the Dirac operator in three dimensions
• Uniform Lieb-Thirring inequality for the three dimensional Pauli operator with a strong non-homogeneous magnetic field
• Magnetic Lieb-Thirring inequalities with optimal dependence on the field strength

Cited by in corpus (2)

• Dirac-Sobolev inequalities and estimates for the zero modes of massless Dirac operators
• Eigenfunctions at the threshold energies of magnetic Dirac operators