Nontransversality of the gluon polarization tensor in a chromomagnetic background field

We investigate the problem of the transversality of the gluon polarization tensor in a homogeneous Abelian chromomagnetic background field. Using the Slavnov–Taylor identities, we rederive the nontransversality known from a one-loop calculation in the Feynman gauge. In addition, we generalize the whole procedure to an arbitrary gauge-fixing parameter $\xi$ and calculate the $\xi$-dependent part of the polarization tensor.