Field-dependent BRST-antiBRST Transformations in Yang-Mills and Gribov-Zwanziger Theories

Understand

We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet $\lambda_{a}$, $a=1,2$, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang-Mills theories.

• It turns out that the finite transformations are quadratic in their parameters.
• At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang-Mills vacuum functional, special field-dependent BRST-antiBRST transformations, with $s_{a}$-potential parameters $\lambda_{a}=s_{a}\Lambda$ induced by a finite even-valued functional $\Lambda$ and by the anticommuting generators $s_{a}$ of BRST-antiBRST transformations, amount to a precise change of the gauge-fixing functional.
• This proves the independence of the vacuum functional under such BRST-antiBRST transformations.