We develop a general gauge-invariant Lagrangian construction for half-integer higher spin fields in the AdS space of any dimension. Starting with a formulation in terms of an auxiliary Fock space, we obtain closed nonlinear symmetry algebras of higher spin fermionic fields in the AdS space and find the corresponding BRST operator. A universal procedure for constructing gauge-invariant Lagrangians describing the dynamics of fermionic fields of any spin is developed. No off-shell constraints for the fields and gauge parameters are imposed from the very beginning. It is shown that all the constraints determining an irreducible representation of the AdS group arise as a consequence of the equations of motion and gauge transformations. As an example of the general procedure, we derive gauge-invariant Lagrangians for massive fermionic fields of spin 1/2 and 3/2 containing the complete set of auxiliary fields and gauge symmetries.
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.
A definition of soft breaking of BRST symmetry in the field-antifield formalism is proposed, valid for general gauge theories and arbitrary gauge fixing. The Ward identities for the generating functionals of Green's functions are derived, and their gauge dependence is investigated. We discuss the Gribov-Zwanziger action for the one-parameter family of R ξ gauges. It is argued that gauge theories with a soft breaking of BRST symmetry are inconsistent.
We construct a Lagrangian description of irreducible integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having k rows, on a basis of the universal BRST approach. Starting with a description of bosonic mixed-symmetry higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space associated with special Poincare module, 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, for the first time, auxiliary representations of the constraint subalgebra, to be isomorphic due to Howe duality to sp(2k) algebra, and containing the subsystem of second-class constraints in terms of new oscillator variables. We propose a universal procedure of constructing unconstrained gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive bosonic fields of any spin. 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. As examples of the general procedure, we formulate the method of Lagrangian construction for bosonic fields subject to arbitrary Young tableaux having 3 rows and derive the gaugeinvariant Lagrangian for new model of massless rank-4 tensor field with spin (2, 1, 1) and second-stage reducible gauge symmetries.
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.
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