Inverse boundary value problems and the Aharonov Bohm effect

We consider the inverse boundary value problem for the Schrödinger equation with electromagnetic or Yang–Mills potentials in multiconnected domains Ω ⊂ R n , n ≥ 2. We prove that if the Dirichlet-to-Neumann operators on ∂Ω are gauge equivalent then the corresponding potentials are gauge equivalent too. The multiconnectedness of Ω leads to the Aharonov–Bohm effect.