The Faddeev-Popov gauge-fixed Yang-Mills Lagrangian is invariant under $$ \bar c\to\bar c+\chi $$ for any odd constant $\chi$. What is the physical interpretation of this invariance? What does this translation transformation correspond to, in practical terms (e.g., at the level of Feynman diagrams)?
Perhaps relevant: this invariance forbids terms quadratic in $\bar cc$, which are necessary for renormalisability if we pick e.g. a gauge-fixing condition of the form $\partial\cdot A+\alpha A^2\equiv 0$ rather than the standard $\partial\cdot A\equiv 0$ one.