论文标题
$ u（n）$ - 连接耦合旋转器的Calderon问题的唯一结果
A Uniqueness Result for the Calderon Problem for $U(N)$-connections coupled to spinors
论文作者
论文摘要
在本文中，我们为扭曲的dirac laplacian定义了一张Dirichlet to-Neumann地图，该图在旋转歧管上作用于束值的纺纱器。我们表明，该地图是订单1的伪数字运算符，其符号确定了边界处的泰勒级数和连接的泰勒级数。我们继续表明，如果通过杨 - 米尔斯 - 迪拉克方程与旋转器具有适当的边界条件，并且具有相等的dirichlet to-neumann映射，则两个连接是局部量规等效的。在阿贝尔情况下，连接是全球量规等效的。
In this paper we define a Dirichlet-to-Neumann map for a twisted Dirac Laplacian acting on bundle-valued spinors over a spin manifold. We show that this map is a pseudodifferential operator of order 1 whose symbol determines the Taylor series of the metric and connection at the boundary. We go on to show that if two real-analytic connections couple to a spinor via the Yang--Mills--Dirac equations with appropriate boundary conditions, and have equal Dirichlet-to-Neumann maps, then the two connections are locally gauge equivalent. In the abelian case, the connections are globally gauge equivalent.
