BRS Transformations Research Articles

Nielsen identities in the 't Hooft gauge

We derive Nielsen identities for the gauge invariance of the effective potential and the physical Higgs mass in the 't Hooft gauge and verify them to one-loop level. In addition to the standard derivation we also show how they may be derived by considering a BRS transformation which acts on the gauge parameter.

Gauge independence in ordinary Yang-Mills theories

Dependence on the gauge parameter α is detected by means of BRS transformations which act also on α. Establishing the corresponding Slavnov identity means controlling gauge dependence at the same time. Simple algebraic manipulation thereby replace the use of Wilson expansions and complete the renormalization scheme independent treatment.

Gauge independence in N = 1 supersymmetric Yang-Mills theories

Supersymmetric gauge theories depend on an infinity of gauge parameters due to the vanishing dimension of the gauge superfields. We show here their non-physical character. The proof is based on a Slavnov identity modified by allowing the gauge parameters to vary under the BRS transformations.

BRS transformation in lattice gauge theories

Using the results of Sharpe on the gauge fixing in lattice gauge theories we construct a lattice version of the BRS transformation. As an application we state the Ward-Takahashi identities on a lattice.

Geometric Description of BRS Transformation for the Fields in P4 Theory

When the BRS transformation of the vierbein fields are defined as Eq. (26), (26) The changes of the following equations (27)˜(31) are unnecessary. The ghost fields cta defined in Eq. (26) correspond to those in the abelian T4 theory.

Representations of BRS algebra

In the canonical formulation of gauge theories the BRS transformation plays a fundamental rôle. The generator of this transformation along with the ghost number forms an algebra called the BRS algebra. Certain properties of this algebra are essential to the proof of unitarity of the S matrix in the physical sector and also to the discussion of color confinement. In the present paper we present all the possible representations of the BRS algebra in the light of indefinite metric.

Some remarks on BRS transformations, anomalies and the cohomology of the Lie algebra of the group of gauge transformations

We show that ghosts in gauge theories can be interpreted as Maurer-Cartan forms in the infinite dimensional group ℊ of gauge transformations. We examine the cohomology of the Lie algebra of ℊ and identify the coboundary operator with the BRS operator. We describe the anomalous terms encountered in the renormalization of gauge theories (triangle anomalies) as elements of these cohomology groups.

Manifestly-covariant canonical formalism of Poincaré gauge theories

We present a general framework for manifestly-covariant canonical formulation of Poincare gauge theories. We construct a general class of action that is invariant under two kinds of BRS transformations—translation and internal Lorentz—and suitable for manifestly-covariant canonical quantization. This theory contains a great number of conserved quantities, which we investigate systematically. It is also pointed out that a canonical formulation of higher-derivative theories may be obtained as a limiting case in this framework.

BRS and Anti-BRS Transformations in GL (4, R) Theory

The BRS and anti-BRS transformations of the fields in GL (4, R) theory are deduced with the aid of the heuristic geometrical formulation.

Geometrical Description of BRS and Anti-BRS Transformations for the Gravitational Fields

On deduit les transformations BRS et anti-BRS pour les champs gravitationnels a partir de considerations geometriques heuristiques

Superfield formalism for gauge theories with ghosts and gauge fixing terms from dynamics on superspace

The geometrical condition of soul-flatness needed in the superfield approach to quantized gauge theories and extended BRS transformations, is derived from a lagrangian theory on a superspace S 4.2. Invariance of the superlagrangian and the lagrangian of quantized gauge theories under Sp(2, R) and hermitian conjugation is discussed in different gauges.

Geometrical interpretation of the BRS transformations of quantum gravity

A geometrical interpretation of ghost fields and BRS transformations in the framework of the metric formulation of quantum gravity is proposed without introducing a superspace.

Superspace approach to the extended BRS symmetries of quantum gravity

A superspace formulation of the BRS and anti-BRS transformations in quantum gravity is given a la Bonora and Tonin. The relation between the present construction and that proposed recently by Hirayama and Hirano is also discussed.

Superspace formulation of BRS transformation of quantum gravity

It is shown that Bonora and Tonin's superspace formulation of the BRS and anti-BRS transformations still works for the theory of quantized gravitational field. The difference between cases of the Yang-Mills field and the gravitational field is discussed.

Kaluza-Klein theory and extended BRS symmetry

It is shown that in the same way as the Kaluza-Klein theory the extended BRS transformation in the (4 + n)-dimensional Einstein theory is consistently decomposed into the sum of the standard extended BRS transformation in the four-dimensional Einstein and Yang-Mills theory.

Comments on massive and massless Yang-Mills lagrangians with a quartic coupling of Faddeev-Popov ghosts

The complicated Lagrangians for massless as well as massive Yang-Mills fields and their BRS and anti-BRS transformations proposed by Curci and Ferrari are simplified by the help of an auxiliary field. In the massive non-Abelian case, the mechanism of the breakdown of physicalS-matrix unitarity is clarified and contrasted to the situation in the Abelian case.

Local OSp(4/2) supersymmetry and extended BRS transformations for gravity

When the gravitational field and its fictitious partners are grouped into anOSp(4/2) supermultiplet, an extended BRS invariance emerges. The action and BRS transformations (ordinary and dual) are written in supersymmetric form, and the extended gauge identities are deduced, in parallel with recent work on Yang-Mills theory.

Extended BRS invariance and OSp (4/2) supersymmetry

A superfield action is proposed within an OSp(4/2) framework whose component form reproduces the covariant xi -gauge Yang-Mills action, but with modified ghost-compensating terms. (The case xi =0 reduces to the usual Landau gauge.) 'Supertranslations' give rise to extended BRS transformations, and lead to constraints amongst the renormalisation constants. In addition, the system admits 'super-Lorentz' transformations, which mix vector and ghost fields. For other field representations, the ghost structure suggested by the space-time supersymmetry OSp(4/G) is also exhibited. This simplifies the results for counting ghosts and their own ghosts.

Kaluza-Klein theory and BRS symmetry

It is shown that the BRS transformation in the higher-dimensional Einstein theory can be consistently decomposed in the way of Kaluza and Klein. We get the standard BRS formalism in the four-dimensional Einstein-Yang-Mills theory.

A dual BRS invariance for gravity?

The dual BRS transformations for vector-meson theories are associated with interchanges of fictitious fields and, apart from minor modification, they are the same as the ordinary transformations. In gravity the authors show that the analogous transformations do not generally lead to an invariance of the action except for an extreme choice of gauge.