  We consider an $\mathcal{MP}$-system, that is, a compact Riemannian manifold
with boundary, endowed with a magnetic field and a potential. On simple
$\mathcal{MP}$-systems, we study the $\mathcal{MP}$-ray transform in order to
obtain new boundary rigidity results for $\mathcal{MP}$-systems. We show that
there is an explicit relation between the $\mathcal{MP}$-ray transform and the
magnetic one, which allow us to apply results from [DPSU07] to our case.
Regarding rigidity, we show that there exists a generic set $\mathcal{G}^{m}$
of simple $\mathcal{MP}$-systems, which is open and dense, such that any two
$\mathcal{MP}$-systems close to an element in it and having the same boundary
action function, must be $k$-gauge equivalent.
