论文标题
磁性超级运算符的演算
A Calculus for Magnetic Pseudodifferential Super Operators
论文作者
论文摘要
这项工作为超级操作员OPA（F）开发了磁性分差计算；这些地图运算符到操作员（与LP功能上的LQ函数相对）。在这里，f可能是钢化的分布或hörmander符号。一个重要的例子是Liouville超级操作员根据磁性差异操作员定义。我们的工作结合了[MP04，IMP07，LEI11]中开发的磁性Weyl微积分的想法，以及来自[HLP18A，HLP18B]的非交换圆环上的伪差分线。因此，我们的演算本质上是衡量的，这意味着OPA（F）的所有必需特性都是由磁场B = DA而不是向量电位A的特性确定的。 普通伪差异理论存在概念差异。例如，除了（磁性）Weyl产物的类似物外，还模仿了两个磁性假数超级算子在函数级别上的组成，所谓的半柔软产品还描述了假数分化超级操作员在假数差操作员上的作用。
This work develops a magnetic pseudodifferential calculus for super operators OpA(F); these map operators onto operators (as opposed to Lp functions onto Lq functions). Here, F could be a tempered distribution or a Hörmander symbol. An important example is Liouville super operators defined in terms of a magnetic pseudodifferential operator. Our work combines ideas from magnetic Weyl calculus developed in [MP04, IMP07, Lei11] and the pseudodifferential calculus on the non-commutative torus from [HLP18a, HLP18b]. Thus, our calculus is inherently gauge-covariant, which means all essential properties of OpA(F) are determined by properties of the magnetic field B = dA rather than the vector potential A. There are conceptual differences to ordinary pseudodifferential theory. For example, in addition to an analog of the (magnetic) Weyl product that emulates the composition of two magnetic pseudodifferential super operators on the level of functions, the so-called semi-super product describes the action of a pseudodifferential super operator on a pseudodifferential operator.
