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We study the inverse boundary value problems for the Schr\"{o}dingerequations with Yang-Mills potentials in a bounded domain $\Omega_0\subset\R^n$containing finite number of smooth obstacles $\Omega_j,1\leq j \leq r$. Weprove that the Dirichlet-to-Neumann operator on $\partial\Omega_0$ determinesthe gauge equivalence class of the Yang-Mills potentials. We also prove thatthe metric tensor can be recovered up to a diffeomorphism that is identity on$\partial\Omega_0$.Comment: 15 page

Inverse problems for Schrödinger equations with Yang–Mills potentials in domains with obstacles and the Aharonov–Bohm effect