Antifield Formalism Research Articles

A general non renormalization theorem in the extended antifield formalism

In the context of algebraic renormalization, the extended antifield formalism is used to derive the general forms of the anomaly consistency condition and of the Callan-Symanzik equation for generic gauge theories. A local version of the latter is used to derive sufficient conditions for the vanishing of beta functions associated to terms whose integrands are invariant only up to a divergence for an arbitrary non trivial non anomalous symmetry of the Lagrangian. These conditions are independent of power counting restrictions and of the form of the gauge fixation.

Irreducible antifield formalism for reducible constrained Hamiltonian systems

Reducible constrained Hamiltonian systems are quantized accordingly an irreducible BRST manner. Our procedure is based on the construction of an irreducible theory which is physically equivalent with the original one. The equivalence between the two systems makes legitimate the substitution of the BRST quantization for the reducible theory by that of the irreducible system. The general formalism is illustrated in detail on a model involving abelian one- and two-form gauge fields.

Anomalous global currents and compensating fields in the BV formalism

We compute the anomalous divergence of currents associated with global transformations in the antifield formalism, by introducing compensating fields that gauge these transformations. We consider the explicit case of the global axial current in QCD but the method applies to any global transformation of the fields.

Irreducible antifield analysis of p-form gauge theories

The irreducible antifield formalism for p-form gauge theories with gauge invariant interaction terms is exposed. The ghosts of ghosts do not appear. The acyclicity of the Koszul-Tate operator is ensured without introducing antifields at resolution degrees higher that two.

BRST antifield treatment of metric-affine gravity

The metric-affine gauge theory of gravity provides a broad framework in which gauge theories of gravity can be formulated. In this article we fit metric-affine gravity into the covariant BRST--antifield formalism in order to obtain gauge fixed quantum actions. As an example the gauge fixing of a general two-dimensional model of metric-affine gravity is worked out explicitly. The result is shown to contain the gauge fixed action of the bosonic string in conformal gauge as a special case.

Extended antifield formalism

The antifield formalism is extended so as to incorporate the rigid symmetries of a given theory. To that end, it is necessary to introduce global ghosts not only for the given rigid symmetries, but also for all the higher order conservation laws, associated with conserved antisymmetric tensors j μ 13 μ k fulfilling ϖ μ 1 j μ 13 μ k 2~ 0. Otherwise, one may encounter obstructions of the type discussed in by the authors. These higher order conservation laws are shown to define additional rigid symmetries of the master equation and to form — together with the standard symmetries — an interesting algebraic structure. They lead furthermore to independent Ward identities which are derived in the standard manner, because the resulting master (“Zinn-Justin”) equation capturing both the gauge symmetries and the rigid symmetries of all orders takes a known form. Issues such as anomalies or consistent deformations of the action preserving some set of rigid symmetries can be also systematically analysed in this framework.

Anti-field formalism and non-Abelian duality

The act of implementing non-Abelian duality in two dimensional sigma models results unavoidably in an additional reducible symmetry. The Batalin-Vilkovisky formalism is employed to handle this new symmetry. Valuable lessons are learnt here with respect to non-Abelian duality. We emphasise, in particular, the effects of the ghost sector corresponding to this symmetry on non-Abelian duality.

Global symmetries in the antifield formalism

In this paper, two things are done. First, it is shown that any global symmetry of a gauge-invariant theory can be extended to the ghosts and the antifields so as to leave invariant the solution of the master equation (before gauge fixing). Second, it is proved that the incorporation of the rigid symmetries to the solution of the master equation through the introduction of a constant ghost for each global symmetry can be obstructed already at the classical level whenever the theory possesses higher order conservation laws. Explicit examples are given.

Some remarks on the BRST quantization of massive Abelian two-form gauge fields.

In this paper we quantize massive Abelian two-form gauge fields in six dimensions following the antifield BRST formalism. The quantization procedure is based on the quantization of a first-class system associated with the original theory. This first-class system is obtained by converting the original second-class constraints into some first-class ones in a way to preserve the reducibility of free Abelian three-form gauge fields. The path integral of the first-class system is identical to the original one in an appropriate gauge-fixing fermion. Finally, it is shown that this first-class system leads to the one derived by Bizdadea and Saliu. \textcopyright{} 1996 The American Physical Society.

Lagrangian Becchi-Rouet-Stora-Tyutin treatment of collective coordinates.

The Becchi-Rouet-Stora-Tyutin (BRST) treatment for the quantization of collective coordinates is considered in the Lagrangian formalism. The motion of a particle in a Riemannian manifold is studied in the case when the classical solutions break a non-Abelian global invariance of the action. Collective coordinates are introduced, and the resulting gauge theory is quantized in the BRST antifield formalism. The partition function is computed perturbatively to two loops, and it is shown that the results are independent of gauge-fixing parameters. \textcopyright{} 1996 The American Physical Society.

Trace anomaly in the field - antifield formalism

The field - antifield quantization method is used to calculate the trace anomaly for a massless scalar field in a curved background, by means of the zeta function regularization procedure.

Local BRST cohomology in Einstein-Yang-Mills theory

We analyse in detail the local BRST cohomology in Einstein-Yang-Mills theory using the antifield formalism. We do not restrict the Lagrangian to be the sum of the standard Hilbert and Yang-Mills Lagrangians, but allow for more general diffeomorphism and gauge invariant (normal) actions. The analysis is carried out in spacetimes with R n topology, for all spacetime dimensions strictly larger than 2 and for all ghost numbers. This covers the classification of all candidate anomalies, of all consistent deformations of the action, as well as the computation of the (equivariant) characteristic cohomology, i.e. the cohomology of the spacetime exterior derivative in the space of (gauge invariant) local differential forms modulo forms that vanish on-shell. We show in particular that for a semi-simple Yang-Mills gauge group the antifield dependence can be entirely removed both from the consistent deformations of the Lagrangian and from the candidate anomalies. Thus, the allowed deformations of the action necessarily preserve the gauge structure, while the only candidate anomalies are those provided by previous works not dealing with antifields, and by “topological” candidate anomalies related to the non-triviality of the manifold of the gravitational variables. This result no longer holds in presence of abelian factors where new candidate anomalies and deformations of the action can be constructed out of the conserved Noether currents (if any). The Noether currents themselves are shown to be covariantizable, i.e. they can be chosen to be invariant under local Lorentz and Yang-Mills transformations and covariant under diffeomorphisms, with a few exceptions discussed as well.

Background gauge invariance in the anti-field formalism for theories with open gauge algebras

We show that any BRST-invariant quantum action with open or closed gauge algebra has a corresponding local background gauge invariance. If the BRST symmetry is anomalous, but the anomaly can be removed in the anti-field formalism, then the effective action possesses a local background gauge invariance. The presence of anti-fields (BRST sources) is necessary. As an example we analyse chiral gravity.

Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory

Yang-Mills models with compact gauge group coupled to matter fields are considered. The general tools developed in a companion paper are applied to compute the local cohomology of the BRST differential $s$ modulo the exterior spacetime derivative $d$ for all values of the ghost number, in the space of polynomials in the fields, the ghosts, the antifields (=sources for the BRST variations) and their derivatives. New solutions to the consistency conditions $sa+db=0$ depending non trivially on the antifields are exhibited. For a semi-simple gauge group, however, these new solutions arise only at ghost number two or higher. Thus at ghost number zero or one, the inclusion of the antifields does not bring in new solutions to the consistency condition $sa+db=0$ besides the already known ones. The analysis does not use power counting and is purely cohomological. It can be easily extended to more general actions containing higher derivatives of the curvature, or Chern-Simons terms.

Local BRST cohomology in the antifield formalism: I. General theorems

We establish general theorems on the cohomologyH * (s/d) of the BRST differential modulo the spacetime exterior derivative, acting in the algebra of localp-forms depending on the fields and the antifields (=sources for the BRST variations). It is shown thatH −k (s/d) is isomorphic toH k (δ/d) in negative ghost degree−k (k>0), where δ is the Koszul-Tate differential associated with the stationary surface. The cohomology groupH 1 (δ/d) in form degreen is proved to be isomorphic to the space of constants of the motion, thereby providing a cohomological reformulation of Noether's theorem. More generally, the groupH k (δ/d) in form degreen is isomorphic to the space ofn−k forms that are closed when the equations of motion hold. The groupsH k (δ/d)(k>2) are shown to vanish for standard irreducible gauge theories. The groupH 2 (δ/d) is then calculated explicitly for electromagnetism, Yang-Mills models and Einstein gravity. The invariance of the groupsH k (s/d) under the introduction of non-minimal variables and of auxiliary fields is also demonstrated. In a companion paper, the general formalism is applied to the calculation ofH k (s/d) in Yang-Mills theory, which is carried out in detail for an arbitrary compact gauge group.

Renormalization of gauge invariant operators and anomalies in Yang-Mills theory.

A long-standing conjecture on the structure of renormalized, gauge invariant, integrated operators of arbitrary dimension in Yang-Mills theory is established. The general solution of the consistency condition for anomalies with sources included is also derived. This is achieved by computing explicitely the cohomology of the full unrestricted BRST operator in the space of local polynomial functionals with ghost number equal to zero or one. The argument does not use power counting and is purely cohomological. It relies crucially on standard properties of the antifield formalism.

Perturbation theory and locality in the field–antifield formalism

The Batalin–Vilkovisky formalism is studied in the framework of perturbation theory by analyzing the antibracket Becchi–Rouet–Stora–Tyutin (BRST) cohomology of the proper solution S0. It is concluded that the recursive equations for the complete proper solution S can be solved at any order of perturbation theory. If certain conditions on the classical action and on the gauge generators are imposed the solution can be taken local.

ON POSSIBLE GENERALIZATIONS OF FIELD-ANTIFIELD FORMALISM

A generalized version is proposed for the field–antifield formalism. The antibracket operation is defined in arbitrary field–antifield coordinates. The antisymmetric definitions are given for first- and second-class constraints. In the case of second-class constraints the Dirac's antibracket operation is defined. The quantum master equation as well as the hypergauge fixing procedure are formulated in a coordinate–invariant way. The general hypergauge functions are shown to be antisymmetric first–class constraints whose Jacobian matrix determinant is constant on the constraint surface. The BRST-type generalized transformations are defined and the functional integral is shown to be independent of the hypergauge variations admitted. In the case of reduced phase space the Dirac's antibrackets are used instead of the ordinary ones.

Extended from method of antifield-BRST formalism for topological quantum field theories

The author presents a concise method to construct a BRST-invariant action for the topological quantum field theories in the Batalin-Vilkovisky antifield formalism. The BV action that is a solution to the master equation is directly obtained by means of the extended forms that involve all the required ghosts and antifields. The BV actions for the non-Abelian BF theories (in four and higher dimensions) and for the Chern-Simons theory are constructed by means of the extended form method. An extension of the BF theory in four dimensions to include a 'cosmological term' is also examined and the close connection with the topological Yang-Mills theory is indicated.

BRST-anti-BRST antifield formalism. The example of the Freedman-Townsend model

The general BRST-anti-BRST construction in the framework of the antifield-antibracket formalism is illustrated in the case of the Freedman-Townsend model.