论文标题
对称的一阶差分系统的必要自动接合度和在$ \ mathbb {r}^d $中限制域上的狄拉克粒子的限制
Essential self-adjointness of symmetric first-order differential systems and confinement of Dirac particles on bounded domains in $\mathbb{R}^d$
论文作者
论文摘要
我们证明了具有Lorentz标量电势的Dirac运算符的必不可少的自动相关性，它们在空间域的边界$ \partialΩ$附近生长得足够快。在途中，我们首先考虑一般对称的一阶差异系统，为此我们确定了一个新的，称为标量电势的新型潜力，以确保基本的自我相关性。此外，在两个维度的情况下，使用狄拉克操作员的超对称结构，我们证明了狄拉克粒子的限制，即操作员的基本自我相关性，仅由磁场$ \ nathcal {b} $假定，假定会增长，接近$ \partialΩ$，均超过$ 1/\ $ 1/\ big（2 \ big） \partialΩ）^2 \ big）$。
We prove essential self-adjointness of Dirac operators with Lorentz scalar potentials which grow sufficiently fast near the boundary $\partialΩ$ of the spatial domain $Ω\subset\mathbb R^d$. On the way, we first consider general symmetric first order differential systems, for which we identify a new, large class of potentials, called scalar potentials, ensuring essential self-adjointness. Furthermore, using the supersymmetric structure of the Dirac operator in the two dimensional case, we prove confinement of Dirac particles, i.e. essential self-adjointness of the operator, solely by magnetic fields $\mathcal{B}$ assumed to grow, near $\partialΩ$, faster than $1/\big(2\text{dist} (x, \partialΩ)^2\big)$.
