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We use boundary triples to find a parametrization of all self-adjointextensions of the magnetic Schr\"odinger operator, in a quasi-convexdomain~$\Omega$ with compact boundary, and magnetic potentials with componentsin $\textrm{W}^{1}_{\infty}(\overline{\Omega})$. This gives also a newcharacterization of all self-adjoint extensions of the Laplacian in nonregulardomains. Then we discuss gauge transformations for such self-adjoint extensionsand generalize a characterization of the gauge equivalence of the Dirichletmagnetic operator for the Dirichlet Laplacian; the relation to theAharonov-Bohm effect, including irregular solenoids, is also discussed. Inparticular, in case of (bounded) quasi-convex domains it is shown that if someextension is unitarily equivalent (through the multiplication by a smooth unitfunction) to a realization with zero magnetic potential, then the same occursfor all self-adjoint realizations.

All self-adjoint extensions of the magnetic Laplacian in nonsmooth domains and gauge transformations