  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.
