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Following our recent study [P.Yu. Moshin, A.A. Reshetnyak, Nucl. Phys. B 888(2014) 92], we discuss the notion of finite BRST-antiBRST transformations, witha doublet $\lambda_{a}$, $a=1,2$, of anticommuting (both global andfield-dependent) Grassmann parameters. It turns out that the global finiteBRST-antiBRST transformations form a 2-parametric Abelian supergroup. We findan explicit Jacobian corresponding to this change of variables in the theorieswith a gauge group. Special field-dependent BRST-antiBRST transformations forthe Yang--Mills path integral with $s_{a}$-potential (functionally-dependent)parameters $\lambda_{a}=s_{a}\Lambda$ generated by a finite even-valuedfunctional $\Lambda$ and the anticommuting generators $s_{a}$ of BRST-antiBRSTtransformations, amount to a precise change of the gauge-fixing functional.This proves the independence of the vacuum functional under such BRST-antiBRSTtransformations and leads to the presence of modified Ward identities. The formof transformation parameters that induces a change of the gauge in the pathintegral is found and is exactly evaluated for connecting two arbitrary$R_{\xi}$-like gauges. The finite field-dependent BRST-antiBRST transformationsare used to generalize the Gribov horizon functional $h_{ 0 }$, in the Landaugauge of the BRST-antiBRST setting in the Gribov--Zwanziger model, and to find$h_{\xi}$ corresponding to general $R_{\xi}$-like gauges in the form compatiblewith a gauge-independent $S$-matrix.

Finite BRST-antiBRST Transformations for the Theories with Gauge Group