Antifield Formalism Research Articles

BRST deformations and stability in the higher derivative Chern–Simons gauge theory

We show the procedure of BRST deformations of the free Chern–Simons gauge theory with the higher derivatives in antifield formalism and obtain the consistent interactions in the master action at different orders. The key ingredient in our analysis is the local BRST-cohomology which plays a crucial role in the determination of the first-order deformation, also the Jacobi identity is needed since it will greatly simplify the calculations for us. Making using of the Dirac’s method, we give a detailed Hamiltonian analysis both for the free and interacting systems and exhibit that the number of physical degrees of freedom is unchanged after the deformation process. Moreover, we demonstrate that the free higher derivative system can be stabilized from the viewpoint of the existence of another bounded conserved quantities which are different from the canonical energy.

On the Cohomological Derivation of Yang-Mills Theory in the Antifield Formalism

We present a brief review of the cohomological solutions of self-coupling interactions of the fields in the free Yang-Mills theory. All consistent interactions among the fields have been obtained using the antifield formalism through several order BRST deformations of the master equation. It is found that the coupling deformations halt exclusively at the second order, whereas higher order deformations are obstructed due to non-local interactions. The results demonstrate the BRST cohomological derivation of the interacting Yang-Mills theory.

General quantum-mechanical setting for field–antifield formalism as a hyper-gauge theory

A general quantum-mechanical setting is proposed for the field–antifield formalism as a unique hyper-gauge theory in the field–antifield space. We formulate a Schrödinger-type equation to describe the quantum evolution in a “current time” purely formal in its nature. The corresponding Hamiltonian is defined in the form of a supercommutator of the delta-operator with a hyper-gauge fermion. The initial wave function is restricted to be annihilated with the delta-operator. The Schrödinger’s equation is resolved in a closed form of the path integral, whose action contains the symmetric Weyl’s symbol of the Hamiltonian. We take the path integral explicitly in the case of a hyper-gauge fermion being an arbitrary function rather than an operator.

New aspects of quantization of the Jackiw–Pi model: field–antifield formalism and noncommutativity

The so‐called Jackiw–Pi (JP) model for massive vector fields is a three‐dimensional, gauge‐invariant and parity‐preserving model that was discussed in several contexts. In this paper we have discussed its quantum aspects through the introduction of Planck‐scale objects, i.e., via noncommutativity and the well‐known BV quantization. Namely, we have constructed the JP noncommutative space‐time version, we have provided the BV quantization of the commutative JP model and we have discussed its features. The noncommutativity has introduced interesting new objects in JP's Planck‐scale framework. image

A systematic study of finite BRST-BV transformations within W–X formulation of the standard and the Sp(2)-extended field–antifield formalism

Finite BRST-BV transformations are studied systematically within the W-X formulation of the standard and the Sp(2)-extended field-antifield formalism. The finite BRST-BV transformations are introduced by formulating a new version of the Lie equations. The corresponding finite change of the gauge-fixing master action X and the corresponding Ward identity are derived.

Hybrid Seiberg-Witten map, itsθ-exact expansion, and the antifield formalism

We deduce an evolution equation for an arbitrary hybrid Seiberg-Witten map for compact gauge groups by using the antifield formalism. We show how this evolution equation can be used to obtain the hybrid Seiberg-Witten map as an expansion, which is $\theta$-exact, in the number of ordinary fields. We compute explicitly this expansion up to order three in the number of ordinary gauge fields and then particularize it to case of the Higgs of the noncommutative Standard Model.

Extended sigma-model in nontrivially deformed field–antifield formalism

We propose an action for the extended sigma-models in the most general setting of the kinetic term allowed in the nontrivially deformed field–antifield formalism. We show that the classical motion equations do naturally take their desired canonical form.

Does the nontrivially deformed field–antifield formalism exist?

We reformulate the Lagrange deformed field–antifield BV-formalism suggested, in terms of the general Euler vector field N generated by the antisymplectic potential. That N generalizes, in a natural anticanonically-invariant manner, the usual power-counting operator. We provide for the "usual" gauge-fixing mechanism as applied to the deformed BV-formalism.

Finite anticanonical transformations in field–antifield formalism

We study the role of arbitrary (finite) anticanonical transformations in the field–antifield formalism and the gauge-fixing procedure based on the use of these transformations. The properties of the generating functionals of the Green functions subjected to finite anticanonical transformations are considered.

On gauge independence for gauge models with soft breaking of BRST symmetry

A consistent quantum treatment of general gauge theories with an arbitrary gauge-fixing in the presence of soft breaking of the BRST symmetry in the field–antifield formalism is developed. It is based on a gauged (involving a field-dependent parameter) version of finite BRST transformations. The prescription allows one to restore the gauge-independence of the effective action at its extremals and therefore also that of the conventional S-matrix for a theory with BRST-breaking terms being additively introduced into a BRST-invariant action in order to achieve a consistency of the functional integral. We demonstrate the applicability of this prescription within the approach of functional renormalization group to the Yang–Mills and gravity theories. The Gribov–Zwanziger action and the refined Gribov–Zwanziger action for a many-parameter family of gauges, including the Coulomb, axial and covariant gauges, are derived perturbatively on the basis of finite gauged BRST transformations starting from Landau gauge. It is proved that gauge theories with soft breaking of BRST symmetry can be made consistent if the transformed BRST-breaking terms satisfy the same soft BRST symmetry breaking condition in the resulting gauge as the untransformed ones in the initial gauge, and also without this requirement.

A systematic study of finite field-dependent BRST-BV transformations in Sp(2) extended field–antifield formalism

In the framework of Sp(2) extended Lagrangian field–antifield BV formalism, we study systematically the role of finite field-dependent BRST-BV transformations. We have proved that the Jacobian of a finite BRST-BV transformation is capable of generating arbitrary finite change of the gauge-fixing function in the path integral.

A systematic study of finite BRST-BV transformations in field–antifield formalism

We study systematically finite BRST-BV transformations in the field–antifield formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.

External sources in field–antifield formalism

We introduce external sources JA directly into the quantum master action W of the field–antifield formalism instead of the effective action. The external sources JA lead to a set of BRST-invariant functions WA that are in antisymplectic involution. As a byproduct, we encounter quasi-groups with open gauge algebras.

Anomalies in the ERG Approach

The antifield formalism adapted in the exact renormalization group is found to be useful for describing a system with some symmetry, especially the gauge symmetry. In the formalism, the vanishing of the quantum master operator implies the presence of a symmetry. The QM operator satisfies a simple algebraic relation that will be shown to be related to the Wess-Zumino condition for anomalies. We also explain how an anomaly contributes to the QM operator.

Path integral formulation with deformed antibracket

We propose how to incorporate the Leites–Shchepochkina–Konstein–Tyutin deformed antibracket into the quantum field–antifield formalism.

REMARKS ON EXISTENCE OF PROPER ACTION FOR REDUCIBLE GAUGE THEORIES

In the field–antifield formalism, we review existence and uniqueness proofs for the proper action in the reducible case. We give two new existence proofs based on two resolution degrees called "reduced antifield number" and "shifted antifield number," respectively. In particular, we show that for every choice of gauge generators and their higher stage counterparts, there exists a proper action that implements them at the quadratic order in the auxiliary variables.

Publisher’s Note: Einsteinian gravity from BRST quantization of a topological action [Phys. Rev. D77, 084020 (2008)

The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background. However, exact vacuum solutions with double duality properties exhibit a `vacuum degeneracy'. By modifying the duality via a scale breaking term, we demonstrate that only Einstein's equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of `dark energy' as well as `dark matter' modeled by a torsion induced quintaxion.

Einsteinian gravity from BRST quantization of a topological action

In order to deduce Einsteinian gravity from a topological action, we start from the metric-free Pontrjagin invariant in four dimensions. Using the Becchi-Rouet-Stora-Tyutin antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature. They correspond to classical instanton type solutions of a curvature-squared model of gravity, in the affine form proposed already by Weyl and Yang. However, the exact vacuum solutions with double duality properties exhibit a ``vacuum degeneracy.'' By modifying the duality of the curvature via scale breaking terms, we demonstrate that only Einstein's equations with an induced cosmological constant of partially topological origin emerge for the macroscopic ``background.''

Einsteinian gravity from a topological action

The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background. However, exact vacuum solutions with double duality properties exhibit a ‘vacuum degeneracy’. By modifying the duality via a scale breaking term, we demonstrate that only Einstein’s equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of ‘dark energy’ as well as ‘dark matter’ modeled by a torsion induced quintaxion.

From the BRST invariant Hamiltonian to the field–antifield formalism

We study the relation between the Lagrangian field–antifield formalism and the BRST invariant phase–space formulation of gauge theories. Starting from the Batalin–Fradkin–Vilkovisky unitarized action, we demonstrate in a deductive way the equivalence of the phase–space, and the Lagrangian field–antifield partition functions for the case of irreducible first rank theories.