BRS Transformations Research Articles

Representation of BRS and full BRS algebra

The explicit construction of modules (irreducible and indecomposable) for the BRS and full BRS algebras are presented. The existence of parent and daughter phenomena provides a natural basis for the introduction of the metric. The structure of BRS and full BRS transformation groups and the corresponding 'Campbell-Housdorff' formulae are discussed. The relevance and genesis of BRS symmetry groups are briefly analysed in the framework of fibre bundles.

FULL PROPAGATORS IN THE BOSONIZED CHIRAL SCHWINGER MODEL

Using the charge of BRS transformation, we obtain Ward-Takahashi identity and full propagators from the BRS invariant bosonized chiral Schwinger model. It is shown from these propagators that there is a massive Proca field and a massless scalar field for a>1, where a is regarded as the bosonization ambiguities. Also, two propagators of Proca and scalar field both have positive norm states.

Stochastic quantization, non-markovian regularization and renormalization

We consider the stochastic quantization of field theories, generalized to suitable non-markovian processes which can be used as an analytic ultraviolet regularization, and also to provide a new approximation scheme for computing critical exponents. We discuss the renormalization procedure for the general case, making use also of the recently introduced methods based on BRS transformations, and we present a general formulation of a background field method for the Langevin equation.

On the “covariantized light-cone” string field theory II

We present a full non-linear BRS transformation which corresponds to one of the generators of the OSp(1, 1|2) or OSp(26, 2|2) algebra using the covariantly extended joining-splitting type interaction vertex functions in open string field theory.

Generalized Noether identities and application to Yang-Mills field theory

We derive generalized Noether identities for a system with noninvariant action integral under an infinite continuous group and deduce the string conservation laws of the system. We give a preliminary application to field theory and discuss the strong conservation laws for the BRS transformation and the weak conservation laws of Yang-Mills fields. The Dirac constraint of the system is examined.

Weyl gauge fixing and BRS symmetry in string theory

The Weyl freedom in string theory is incorporated into the BRS symmetry in the conformal-type gauge fixing. This clarifies the origins of the requirements such as D = 26 and the intercept condition. The physical equivalence of the reparametrization invariant and Weyl invariant path integral measures at D = 26 is established. The anomaly associated with the BRS transformation is explicitly evaluated, and the possible theory at D < 26 from the BRS viewpoint is also briefly discussed.

BRS symmetry of supergravity in superspace and its projection to component formalism

The BRS symmetry of supergravity theories is geometrically constructed in superspace. The construction is formally identical to the one which holds for gauge theories coupled to gravity. If the classical superspace constraints associated to a given set of auxiliary fields are known it is possible to obtain by projection the whole set of BRS transformation laws in component formalism. We illustrate the method with various representations of N = 1, D = 4 Poincaré supergravity. In particular we consider couplings of Chern-Simons forms. Our analysis proves the absence of U(1) anomaly in the new minimal supergravity for any coupling of matter fields.

BRS anomaly in the fully quantized non-abelian gauge theory

The form of a possible anomalous term in Slavnov-Taylor identities of Yang-Mills theory is determined by making use of a cohomological exact sequence and the same method is applied to the theory with an anti-symmetric tensor gauge field. In both cases the unique anomalous term has the same form as the conventional non-abelian anomaly. The effect of the anomaly on the nilpotency of the BRS transformation is discussed also.

Nielsen identities for gauge-fixing vectors and composite effective potentials

We show how to derive the Nielsen identities which govern the gauge dependence of physical quantities and the effective action for the gauge fixing vectors in both the 't Hooft gauge and in the planar gauge by using an extended set of BRS transformations. We also show that it is possible to derive the identities for an effective action which depends on composite operators.

On the quantization of supersymmetric particle

The modified action of Siegel for a point superparticle is quantized by using the BRS transformation. We also present another action for a superparticle. We discuss the second-quantization of a superparticle and then point out some difficulties in the covariant second quantization of superstring.

Extended BRS-symmetry and the axial gauge in pure Yang-Mills theories

The question of gauge dependence and the structure of possible counter-terms in generalized axial (non light-cone) gauges is studied by means of BRS transformations augmented to include variations of the gauge parameters.

Higher spin fields with mixed symmetry

Gauge invariant and gauge fixed BRS invariant actions are constructed in arbitrary dimensions for free massless integer spin fields carrying mixed representations of the Lorentz group described by Young tableaux (2, 1, 1, …, 1) n . The complete ghost spectrum is deduced by demanding nilpotency of the BRS transformations and leads to a correct count of the on-shell degrees of freedom. Dimensional reduction is used to study the corresponding gauge invariant massive theory. On-shell consistency is then ensured by the fact that the masses arise via a “telescopic Higgs effect”.

Manifestly covariant field theory of interacting string II

Abstract A manifestly covariant field theory is constructed for the interacting bosonic open string. A very simple string action is presented which is invariant under an inhomogeneous nilpotent BRS transformation. The on-shell scattering amplitudes in this theory reproduce the Koba-Nielsen amplitudes at the tree level, aside from a contributions from a necessary quartic interaction term.

Manifestly covariant field theory of interacting string I

A manifestly covariant field theory is constructed for the interacting bosonic open string. A very simple string action is presented which is invariant under an inhomogeneous nilpotent BRS transformation. The on-shell scattering amplitudes in this theory reproduce the Koba-Nielsen amplitudes at the tree level, aside from a contributions from a necessary quartic interaction term.

Universal connections, gauge anomalies and Lie group cohomology

The geometric interpretation, due to Thierry-Mieg (1980) of the ghost field as certain components of an Ehresmann connection on the total space of a principal bundle, and of the BRS transformation as part of the exterior derivative on the total space, is discussed and amended to incorporate the spacetime dependence of the ghost field. Using this interpretation it is shown that non-trivial solutions to the Wess-Zumino consistency condition for gauge anomalies are related to non-trivial de Rham cohomology of the Lie group.

A differential geometric setting for BRS transformations and anomalies II

Complement to our mathematical description of Becchi-Rouet-Stora relations and anomalies of gauge fields (cf. paper with the same title, part I). We treat the case where the structure group is given as a group of matrices, and provide an alternative description of the cohomology governing anomalies in terms of equivariant differential forms on the gauge group.

A differential geometric setting for BRS transformations and anomalies I

The Becchi-Rouet-Stora relations and the cohomological construction of anomalies of gauge fields are described within the theory of principal connections of smooth vector bundles.

ON THE GEOMETRY OF BRS TRANSFORMATIONS AND GAUGE FIXING

ON THE GEOMETRY OF BRS TRANSFORMATIONS AND GAUGE FIXING

Canonical setting of ghosts fields and BRS transformations

We construct a canonical extended phase over the Gauss surface giving directly the ghosts fields for Yang-Mills theory and showing that the BRS transformations are a family of canonical transformations generated by the momentum map of the lifted action of the group of gauge transformations to that space.

Electromagnetic properties of theZ boson. I

Using the invariance under BRS transformations we derive Ward identities for theZ γ γ andZZ γ Green's functions. Anomalous contributions to these identities are also obtained using the path integral formalism. The results agree with our previous calculation in perturbation theory.