Renormalization of non-Abelian gauge theories in a background-field gauge. I. Green's functions

The renormalization of non-Abelian gauge theories is studied in the background-field gauge by means of Ward-Slavnov identities derived from supergauge transformations and with use of 't Hooft and Veltman's renormalization. As a result, the counterterm depending on the background field only is shown to be ${\left(\frac{g}{g_0}\right)}^2\mathcal{L}\left({\overrightarrow{\mathrm{A}}}^{\mathrm{cl}}\right)$.