论文标题
在单层边界积分运算符上
On the single layer boundary integral operator for the Dirac equation
论文作者
论文摘要
本文致力于分析单层边界积分运算符$ \ Mathcal {C} _z $在两维情况下Dirac方程的分析。地图$ \ MATHCAL {C} _Z $是具有奇异的积分运算符，具有免费的Dirac Operator $ a_0 $和$ z $的分解的积分内核属于$ a_0 $的分解集。在平滑边界的情况下，分析了“正”和“负”部分中$ \ Mathcal {C} _z $的分解。获得的结果可以应用于以奇异静电，洛伦兹标量和以关键方式组合的异常磁相互作用的狄拉克运算符。
This paper is devoted to the analysis of the single layer boundary integral operator $\mathcal{C}_z$ for the Dirac equation in the two- and three-dimensional situation. The map $\mathcal{C}_z$ is the strongly singular integral operator having the integral kernel of the resolvent of the free Dirac operator $A_0$ and $z$ belongs to the resolvent set of $A_0$. In the case of smooth boundaries fine mapping properties and a decomposition of $\mathcal{C}_z$ in a 'positive' and 'negative' part are analyzed. The obtained results can be applied in the treatment of Dirac operators with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions that are combined in a critical way.
