论文标题
哪些磁场支持零模式？
Which magnetic fields support a zero mode?
论文作者
论文摘要
本文提出了一些有关磁场大小的结果，这些磁场的大小支持三维迪拉克方程的零模式以及旋转方程的相关问题。众所周知的事实是，要使Schrödinger在三个维度上具有负能量结合状态，该电位的3/2-规范必须大于Sobolev常数。我们证明存在零模式的类似结果，即磁场的3/2-标准必须大于Sobolev常数的两倍。这里的新点是，波函数的旋转性质至关重要。它导致了界限的改善的磁性不平等。虽然结果可能并不尖锐，但在结果确实是最佳的情况下，分析了其他方程式。
This paper presents some results concerning the size of magnetic fields that support zero modes for the three dimensional Dirac equation and related problems for spinor equations. It is a well known fact that for the Schrödinger in three dimensions to have a negative energy bound state, the 3/2- norm of the potential has to be greater than the Sobolev constant. We prove an analogous result for the existence of zero modes, namely that the 3/2 - norm of the magnetic field has to greater than twice the Sobolev constant. The novel point here is that the spinorial nature of the wave function is crucial. It leads to an improved diamagnetic inequality from which the bound is derived. While the results are probably not sharp, other equations are analyzed where the results are indeed optimal.
