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The Batalin–Fradkin–Tyutin (BFT) scheme, which is an improved version of Dirac quantization, is applied to the CP¹ model, and the compact form of a nontrivial first-class Hamiltonian is directly obtained by introducing the BFT physical fields. We also derive a BRST-invariant gauge fixed Lagrangian through the standard path-integral procedure. Furthermore, performing collective coordinate quantization we obtain energy spectrum of rigid rotator in the CP¹ model. Exploiting the Hopf bundle, we also show that the CP¹ model is exactly equivalent to the O(3) nonlinear sigma model at the canonical level.

The Sp(3) BRST symmetry for Yang–Mills theory is derived in the framework of the antibracket–antifield formalism.

We demonstrate that the Hamiltonian structure and the integrability of a system of evolution equations can be formulated in terms of a classical field theory using BRST and anti-BRST symmetries. We derive the field theory action and explicitly generate the integrable hierarchy associated to a bi-Hamiltonian system based on cohomological arguments and gauge-fixing deformations.

We study a free particle system residing on a torus to investigate its Becci–Rouet–Stora–Tyutin symmetries associated with its Stückelberg coordinates, ghosts and anti-ghosts. By exploiting zeibein frame on the toric geometry, we evaluate energy spectrum of the system to describe the particle dynamics. We also investigate symplectic structures involved in the free particle system on the torus.

We derive the different forms of BRST symmetry by using the Batalin–Fradkin–Vilkovisky formalism in a rigid rotor. The so-called "dual-BRST" symmetry is obtained from the usual BRST symmetry by making a canonical transformation in the ghost sector. On the other hand, a canonical transformation in the sector involving Lagrange multiplier and its corresponding momentum leads to a new form of BRST as well as dual-BRST symmetry.

We exploit the 't Hooft–Polyakov monopole to construct closed algebra of the quantum field operators and the BRST charge Q_BRST. In the first-class configuration of the Dirac quantization, by including the Q_BRST-exact gauge-fixing term and the Faddeev–Popov ghost term, we find the BRST invariant Hamiltonian to investigate the de Rham type cohomology group structure for the monopole system. The Bogomol'nyi bound is also discussed in terms of the first-class topological charge defined on the extended internal two-sphere.

We derive the various forms of BRST symmetry using Batalin–Fradkin–Vilkovisky approach in the case of Abelian 2-form gauge theory. We show that the so-called dual BRST symmetry is not an independent symmetry but the generalization of BRST symmetry obtained from the canonical transformation in the bosonic and ghost sector. We further obtain the new forms of both BRST and dual-BRST symmetry by making a general transformation in the Lagrange multipliers of the bosonic and ghost sector of the theory.

We continue investigation of soft breaking of BRST symmetry in the Batalin–Vilkovisky (BV) formalism beyond regularizations like dimensional ones used in our previous paper [JHEP 1110, 043 (2011)]. We generalize a definition of soft breaking of BRST symmetry valid for general gauge theories and arbitrary gauge fixing. The gauge dependence of generating functionals of Green's functions is investigated. It is proved that such introduction of a soft breaking of BRST symmetry into gauge theories leads to inconsistency of the conventional BV formalism.

We study a dependence of Green's functions for the Curci–Ferrari model on the parameter resembling the gauge parameter in massless Yang–Mills theories. It is shown that the on-shell generating functional of vertex functions (effective action) depends on this parameter.

The concept of (global) gauge symmetry breaking plays an important role in many areas of physics. Since the corresponding symmetry is a gauge symmetry, its breaking is actually gauge-dependent. Thus, it is possible to design gauges which restore the symmetry as good as possible. Such gauge constructions will be detailed here, illustrated with the use of lattice gauge theory. Their use will be discussed for the cases of the Higgs effect, high-baryon density color superconductors, and BRST symmetry.

In this paper, we study the gauge invariance of the third quantized supergroup field cosmology which is a model for multiverse. Further, we propose both the infinitesimal (usual) as well as the finite superfield-dependent BRST symmetry transformations which leave the effective theory invariant. The effects of finite superfield-dependent BRST transformations on the path integral (so-called void functional in the case of third quantization) are implemented. Within the finite superfield-dependent BRST formulation, the finite superfield-dependent BRST transformations with specific parameter switch the void functional from one gauge to another. We establish this result for the most general gauge with the help of explicit calculations which holds for all possible sets of gauge choices at both the classical and the quantum levels.

In this paper, we will analyze the breaking of Lorentz symmetry using aether superspace. We will analyze the aether deformation of a Chern–Simons theory using this deformed superspace. As this theory, will have gauge symmetry, we will add gauge and ghost terms to the original action. We will analyze the nonlinear BRST symmetry for this theory. We also analyze the quantum BRST symmetry in BV formalism.

We describe the gauge invariant BRST formulation of a particle constrained to move in a general conic. The model considered constitutes an explicit example of an originally second-class system which can be quantized within the BRST framework. We initially impose the conic constraint by means of a Lagrange multiplier leading to a consistent second-class system which generalizes previous models studied in the literature. After calculating the constraint structure and the corresponding Dirac brackets, we introduce a suitable first-order Lagrangian, the resulting modified system is then shown to be gauge invariant. We proceed to the extended phase space introducing fermionic ghost variables, exhibiting the BRST symmetry transformations and writing the Green’s function generating functional for the BRST quantized model.

We identify a strong similarity among several distinct originally second-class systems, including both mechanical and field theory models, which can be naturally described in a gauge-invariant way. The canonical structure of such related systems is encoded into a gauge-invariant generalization of the quantum rigid rotor. We perform the BRST symmetry analysis and the BFV functional quantization for the mentioned gauge-invariant version of the generalized quantum rigid rotor. We obtain different equivalent effective actions according to specific gauge-fixing choices, showing explicitly their BRST symmetries. We apply and exemplify the ideas discussed to two particular models, namely, motion along an elliptical path and the $O(N)$ nonlinear sigma model, showing that our results reproduce and connect previously unrelated known gauge-invariant systems.

The Lagrangian Sp(3) BRST symmetry for irreducible gauge theories is constructed in the framework of homological perturbation theory. The canonical generator of this extended symmetry is shown to exist. A gauge-fixing procedure specific to the standard antibracket–antifield formalism, that leads to an effective action, which is invariant under all the three differentials of the Sp(3) algebra, is given.

Consistent couplings among a set of scalar fields, two types of one-forms and a system of two-forms are investigated in the light of the Hamiltonian BRST cohomology, giving a four-dimensional nonlinear gauge theory. The emerging interactions deform the first-class constraints, the Hamiltonian gauge algebra, as well as the reducibility relations.

We couple three-dimensional Chern–Simons gauge theory with BF theory and study deformations of the theory by means of the antifield BRST formalism. We analyze all possible consistent interaction terms for the action under physical requirements and find a new topological field theory in three dimensions with new nontrivial terms and a nontrivial gauge symmetry. We analyze the gauge symmetry of the theory and point out the theory that has the gauge symmetry based on the Courant algebroid.

All consistent interactions in a three-dimensional theory with tensor gauge fields of degrees two and three are obtained by means of the deformation of the solution to the master equation combined with cohomological techniques. The local BRST cohomology of this model allows the deformation of the Lagrangian action, accompanying gauge symmetries and gauge algebra. The relationship with the Chern–Simons theory is discussed.

The main BRST cohomological properties of a free, massless tensor field that transforms in an irreducible representation of GL(D,ℝ), corresponding to a rectangular, two-column Young diagram with k>2 rows are studied in detail. In particular, it is shown that any nontrivial co-cycle from the local BRST cohomology group H(s|d) can be taken to stop either at antighost number (k+1) or k, its last component belonging to the cohomology of the exterior longitudinal derivative H(γ) and containing nontrivial elements from the (invariant) characteristic cohomology H^inv (δ|d).

Consistent interactions that can be added to a two-dimensional, free Abelian gauge theory comprising a special class of BF-type models and a collection of vector fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. The deformation procedure modifies the Lagrangian action, the gauge transformations, as well as the accompanying algebra of the interacting model.