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.

We construct a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with the corresponding Young tableaux having two rows, on a basis of the BRST approach. Starting with a description of fermionic higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a first-class constraint system. For this purpose, we find auxiliary representations of the constraint subsuperalgebra containing the subsystem of second-class constraints in terms of Verma modules. We propose a universal procedure of constructing gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive fermionic fields of any spin. No off-shell constraints for the fields and gauge parameters are used from the very beginning. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by the constraints corresponding to an irreducible Poincare-group representation. To illustrate the general construction, we obtain a Lagrangian description of fermionic fields with generalized spin (3/2,1/2) and (3/2,3/2) on a flat background containing the complete set of auxiliary fields and gauge symmetries. * Ramond-Ramond background [29,30] and the conformal N = 4 SYM theory in the context of the AdS/CFT correspondence [31].At present, the dynamics of totally symmetric higher-spin fields presents the most developed direction in the variety of unitary representations of the Poincare and AdS algebras [2,3,16,17,21]. To a great extent, this is caused by the fact that in a 4d space-time there is no place for mixedsymmetry irreducible representations with the exception of dual theories 1 . In higher space-time dimensions, there appear mixed-symmetry representations determined by more than one spinlike parameters, and the problem of their field-theoretic description is not so well-developed as for totally symmetric irreps. Starting from the papers of Fierz-Pauli and Singh-Hagen [1, 2] for higher-spin field theories in the Minkowski space, it has been known that all such theories include, together with the basic fields of a given spin, also some auxiliary fields of lower spins, necessary to provide a compatibility of the Lagrangian equations of motion with the relations that determine irreducible representations of the Poincare group. Attempts to construct Lagrangian descriptions of free and interacting higher-spin field theories have resulted in consistency problems, which are not completely resolved until now.The present work is devoted to the construction of gauge-invariant Lagrangians for both massless and massive mixed-symmetry spin-tensor fields of rank n 1 + n 2 + ... + n k , with any integer numbers n 1 ≥ n 2 ≥ ... ≥ n k ≥ 1 for k = 2 in a d-dimensional Minkowski space, the fields being elements of Poincare-group irreps with a Young tableaux...

We consider two-dimensional gravity with dynamical torsion in the BV and BLT formalisms of gauge theories quantization as well as in the background field method. *

We continue our research Nucl.Phys B888, 92 (2014); Int. J. Mod. Phys. A29, 1450159 (2014); Phys. Lett. B739, 110 (2014); Int. J. Mod. Phys. A30, 1550021 (2015) and extend the class of finite BRST-antiBRST transformations with odd-valued parameters λa, a = 1, 2, introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRST-antiBRST transformations linear in functionally-dependent parameters, as well as those induced by finite BRST-antiBRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with first-class constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRST-antiBRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionally-dependent parameters that implies a modified compensation equation, which admits non-trivial solutions leading to a Jacobian equal to unity. Finite BRST-antiBRST transformations with functionally-dependent parameters are applied to the Standard Model, and an explicit form of functionally-dependent parameters λa is obtained, providing the equivalence of path integrals in any 3-parameter R ξ -like gauges. The Gribov-Zwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in R ξ -like gauges, in a gauge-independent way using field-dependent BRST-antiBRST transformations, and in R ξ -like gauges using transverse-like non-Abelian gauge fields.Recently, in the articles [1,2,3,4], we have proposed an extension of BRST-antiBRST transformations [5,6,7,8] to the case of finite (both global and field-dependent) parameters for Yang-Mills and general gauge theories in the framework of the generalized Hamiltonian [9, 10] -see also 13,14] BRST-antiBRST quantization schemes. The idea of "finiteness" incorporates into finite transformations a new term being quadratic in the transformation parameters λ a , thereby lifting BRST-antiBRST transformations from the algebraic level to the * moshin@rambler.ru † reshet@ispms.tsc.ru 1 group level, which has been discussed also in [15,16]. BRST transformations [17,18,19] in both the Lagrangian [20,21] and generalized Hamiltonian [19, 22, 23] quantization schemes -described by a single odd-valued parameter µ and trivially lifted from the algebraic formwith ← − s 2 = 0, in view of the nilpotency property µ 2 = 0 -have first been suggested in Yang-Mills theories for fielddependent parameters in [24,25]; see also [26,27]. The introduction of such transformations is based on a functional equation for the infinitesimal parameter, providing the invariance of the integrand of the vacuum functional (in the path integral representation based on the Faddeev-Popov rules [28...