Complex Variables and Elliptic Equations ( IF 0.6 ) Pub Date : 2020-12-06 , DOI: 10.1080/17476933.2020.1851211 Vladimir Rabinovich 1
ABSTRACT
We consider the 3-D Dirac operator with variable regular magnetic and electrostatic potentials, and singular potentials (1) (1) where (2) (2) is the singular potential with being a matrix and is the delta-function with support on a surface which divides on two open domains with the common boundary Σ, is a vector-function on with values in are the standard Dirac matrices. We associate with the formal Dirac operator an unbounded operator in generated by with domain in consisting of functions satisfying transmission conditions on Σ. We consider the self-adjointness of operator , its Fredholm properties, and the essential spectrum in the case if Σ is either a closed -surface or an unbounded -hypersurface with a regular behaviour at infinity.
As application we consider the electrostatic and Lorentz scalar δ-shell interactions.
中文翻译:
具有正则和奇异势的 3-D Dirac 算子的 Fredholm 性质和本质谱
摘要
我们考虑具有可变规则磁势和静电势以及奇异势的 3-D Dirac 算子(1)(1)哪里(2)(2) 是奇异势成为一个矩阵和是表面上支持的 delta 函数哪个划分在两个开放域上与公共边界 Σ,是一个向量函数与值是标准狄拉克矩阵。我们与正式的狄拉克算子相关联无界算子在由产生域在由满足 Σ 上的传输条件的函数组成。我们考虑算子的自伴随性,它的 Fredholm 属性,以及如果 Σ 是闭合的情况下的本质谱-表面或无界-在无穷远处具有规律行为的超曲面。
作为应用,我们考虑静电和洛伦兹标量δ -壳相互作用。