  We study the polarization and dispersion properties of gluons moving within a
weakly magnetized background at one-loop order. To this end, we show two
alternative derivations of the charged fermion propagator in the weak field
expansion and use this expression to compute the lowest order magnetic field
correction to the gluon polarization tensor. We explicitly show that, in spite
of its cumbersome appearance, the gluon polarization tensor is transverse as
required by gauge invariance. We also show that none of the three polarization
modes develops a magnetic mass and that gluons propagate along the light cone,
non withstanding that Lorentz invariance is lost due to the presence of the
magnetic field. By comparing with the expression for the gluon polarization
tensor valid to all orders in the magnetic field, the existence of a second
solution, corresponding to a finite gluon mass, is shown to be spurious and an
artifact of the lowest order approximation in the field strength. We also study
the strength of the polarization modes for real gluons. We conclude that,
provided the spurious solutions are discarded, the lowest order approximation
to the gluon polarization and dispersion properties is good as long as the
field strength is small compared to the loop fermion mass.
