  We study the role of the Schwinger phase (SP) that appears in the propagator
of a charged particle in the presence of a static and uniform magnetic field
$\vec{B}$. We first note that this phase cannot be removed by a gauge
transformation; far from this, we show that it plays an important role in the
restoration of the symmetries of the system. Next, we analyze the effect of SPs
in the one-loop corrections to charged pion and rho meson selfenergies. To
carry out this analysis we consider first a simple form for the meson-quark
interactions, and then we study the $\pi^+$ and $\rho^+$ propagators within the
Nambu-Jona-Lasinio model, performing a numerical analysis of the $B$ dependence
of meson lowest energy states. For both $\pi^+$ and $\rho^+$ mesons, we compare
the numerical results arising from the full calculation -- in which SPs are
included in the propagators, and meson wavefunctions correspond to states of
definite Landau quantum number -- and those obtained within alternative schemes
in which SPs are neglected (or somehow eliminated) and meson states are
described by plane waves of definite four-momentum.
