论文标题
DIRAC方程零模式的尖锐标准
A sharp criterion for zero modes of the Dirac equation
论文作者
论文摘要
结果表明，$ \ vert a \ vert_ {l^d}^2 \ ge \ frac {d} {d-2} {d-2} \，s_d $是存在dirac方程$γ\ cdot（-i \ nabla -a-a）$ d $ d $ d $ d $ d $ dimensions的非平凡解决方案的必要条件。在这里，$ s_d $是尖锐的sobolev常数。如果$ d $是奇数，并且$ \ vert a \ vert_ {l^d}^2 = \ frac {d} {d-2} {d-2} \，s_d $，则存在允许零模式的向量电势。给出了这些向量电位及其相应的零模式的完整分类。
It is shown that $\Vert A \Vert_{L^d}^2 \ge \frac{d}{d-2}\, S_d$ is a necessary condition for the existence of a nontrivial solution of the Dirac equation $γ\cdot (-i\nabla -A)ψ= 0$ in $d$ dimensions. Here, $S_d$ is the sharp Sobolev constant. If $d$ is odd and $\Vert A \Vert_{L^d}^2= \frac{d}{d-2}\, S_d$, then there exist vector potentials that allow for zero modes. A complete classification of these vector potentials and their corresponding zero modes is given.
