2022/04/11 by Carlos Valéro, Valero, Carlos
Mathematics · #Spectral Theory in Mathematical Physics #Advanced Operator Algebra Research #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2204.04854
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.