  The experimental progress in synthesizing low-dimensional nanostructures
where carriers are confined to bent surfaces has boosted the interest in the
theory of quantum mechanics on curved two-dimensional manifolds. It was
recently asserted that constrained electrically charged particles couple to a
term linear in A_3 M, where A_3 is the transversal component of the
electromagnetic vector potential and M the surface mean curvature, thereby
making a dimensional reduction procedure impracticable in the presence of
fields. Here we resolve this apparent paradox by providing a consistent general
framework of the thin-wall quantization procedure. We also show that the
separability of the equation of motions is not endangered by the particular
choice of the constraint imposed on the transversal fluctuations of the
wavefunction, which renders the thin-wall quantization procedure well-founded.
It can be applied without restrictions.
