Lagrangian quantization rules for general gauge theories are proposed on a basis of a superfield formulation of the standard BRST symmetry. Independence of the S-matrix on a choice of the gauge is proved. The Ward identities in terms of superfields are derived.

We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet λ 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 λ a = s a Λ induced by a finite even-valued functional Λ and by the anticommuting generators s a of BRST-antiBRST transformations, amount to a precise change of the gaugefixing functional. This proves the independence of the vacuum functional under such BRST-antiBRST transformations. We present the form of transformation parameters that generates a change of the gauge in the path integral and evaluate it explicitly for connecting two arbitrary R ξ -like gauges. For arbitrary differentiable gauges, the finite field-dependent BRST-antiBRST transformations are used to generalize the Gribov horizon functional h, given in the Landau gauge, and being an additive extension of the YangMills action by the Gribov horizon functional in the Gribov-Zwanziger model. This generalization is achieved in a manner consistent with the study of gauge independence. We also discuss an extension of finite BRST-antiBRST transformations to the case of general gauge theories and present an ansatz for such transformations.

We propose a modification of the gauge-fixing procedure in the Lagrangian method of superfield BRST quantization for general gauge theories, which simultaneously provides a natural generalization of the well-known BV quantization scheme as far as gauge-fixing is concerned. A superfield form of BRST symmetry for the vacuum functional is found. The gauge-independence of the S-matrix is established.

We continue the study of finite BRST-antiBRST transformations for general gauge theories in Lagrangian formalism initiated in [1], with a doublet λ a , a = 1, 2, of anticommuting Grassmann parameters, and find an explicit Jacobian corresponding to this change of variables for constant λ a . This makes it possible to derive the Ward identities and their consequences for the generating functional of Green's functions. We announce the form of the Jacobian (proved to be correct in [31]) for finite field-dependent BRSTantiBRST transformations with functionally-dependent parameters, λ a = s a Λ, induced by a finite evenvalued functional Λ(φ, π , λ) and by the generators s a of BRST-antiBRST transformations, acting in the space of fields φ, antifields φ * a , φ and auxiliary variables π a , λ. On the basis of this Jacobian, we present and solve a compensation equation for Λ, which is used to achieve a precise change of the gauge-fixing functional for an arbitrary gauge theory. We derive a new form of the Ward identities, containing the parameters λ a , and study the problem of gauge-dependence. The general approach is exemplified by the Freedman-Townsend model of a non-Abelian antisymmetric tensor field.

We continue our study of finite BRST-anti-BRST transformations for general gauge theories in Lagrangian formalism, initiated in [arXiv:1405.0790 [hep-th] and arXiv:1406.0179 [hep-th]], with a doublet λa, a = 1, 2, of anticommuting Grassmann parameters, and prove the correctness of the explicit Jacobian in the partition function announced in [arXiv:1406.0179 [hep-th]], which corresponds to a change of variables with functionally dependent parameters λa = UaΛ induced by a finite Bosonic functional Λ(φ, π, λ) and by the anticommuting generators Ua of BRST-anti-BRST transformations in the space of fields φ and auxiliary variables π a , λ. We obtain a Ward identity depending on the field-dependent parameters λa and study the problem of gauge dependence, including the case of Yang-Mills theories. We examine a formulation with BRST-anti-BRST symmetry breaking terms, additively introduced into the quantum action constructed by the Sp(2)-covariant Lagrangian rules, obtain the Ward identity and investigate the gauge independence of the corresponding generating functional of Green's functions. A formulation with BRST symmetry breaking terms is developed. It is argued that the gauge independence of the above generating functionals is fulfilled in the BRST and BRST-anti-BRST settings. These concepts are applied to the average effective action in Yang-Mills theories within the functional renormalization group approach.