On a class of Lagrangian models for massive and massless Yang-mills fields

Curci, G; Ferrari, R.

doi:10.1007/bf02729999

Cited by 264 publications

(318 citation statements)

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“…Though all these seemed to rule out the possibility thatc and c can be interchanged, a nilpotent 'antiBRST' transformation symmetry in which this is exactly what happens was introduced long ago [28][29][30]. Indeed, the antiBRST transformations can be obtained from the BRST ones of Eq.…”

Section: Anti-brst Symmetry and The Bfmmentioning

confidence: 99%

“…On the other hand, as both s ands are nilpotent, the additional (natural) requirement that their sum is also nilpotent (or that {s,s} = 0), results in the constraint [28] …”

Section: Anti-brst Symmetry and The Bfmmentioning

confidence: 99%

“…Using then the identifications (3.11), and reintroducing the background-quantum splitting, one obtains the familiar background-quantum identities [45,46] 28) where the color (δ ab ) and Lorentz (P µν ) structures have been factored out. If we are interested only in the UV part of this identity one can set q 2 = 0, thus obtaining 4…”

Section: B Two-point Gluon Sectormentioning

confidence: 99%

“…Indeed, since the advent of BRST quantization, it has been known that a further symmetry exists, induced by an antiBRST transformation [28][29][30] in which the antighost field takes the place of the ghost in the variation of the gauge and matter fields of the theory.…”

Section: Introductionmentioning

confidence: 99%

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Anti-BRST symmetry and background field method

Binosi¹,

Quadri²

2013

Phys. Rev. D

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We show that the requirement that a SU(N) Yang-Mills action (gauge fixed in a linear covariant gauge) is invariant under both the Becchi-Rouet-Stora-Tyutin (BRST) symmetry as well as the corresponding antiBRST symmetry, automatically implies that the theory is quantized in the (linear covariant) background field method (BFM) gauge. Thus, the BFM and its associated background Ward identity naturally emerge from antiBRST invariance of the theory and need not be introduced as an ad hoc gauge fixing procedure. Treating ghosts and antighosts on an equal footing, as required by a BRST-antiBRST invariant formulation of the theory, gives also rise to a local antighost equation that together with the local ghost equation completely resolve the algebraic structure of the ghost sector for any value of the gauge fixing parameter. We finally prove that the background fields are stationary points of the background effective action obtained when the quantum fields are integrated out.

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Section: Anti-brst Symmetry and The Bfmmentioning

confidence: 99%

“…On the other hand, as both s ands are nilpotent, the additional (natural) requirement that their sum is also nilpotent (or that {s,s} = 0), results in the constraint [28] …”

Section: Anti-brst Symmetry and The Bfmmentioning

confidence: 99%

Section: B Two-point Gluon Sectormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Anti-BRST symmetry and background field method

Binosi¹,

Quadri²

2013

Phys. Rev. D

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“…It is not clear at present how these constructions could be adapted to the case of broken BRST symmetry which we have assumed here from the outset. In fact, adding a gluon mass term to the Yang-Mills action gives rise to a Curci-Ferrari model [10] which is perturbatively renormalizable, but is commonly considered not to be unitary [11]. We should like to point out that the statement of non-unitarity refers to the standard construction of the Hilbert space, and it has actually not been shown that no Hilbert space construction exists that would lead to a unitary theory.…”

mentioning

confidence: 99%

Callan-Symanzik equations for infrared Yang-Mills theory

Weber

Dall’Olio

2017

EPJ Web Conf.

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Abstract. Dyson-Schwinger equations have been successful in determining the correlation functions in Yang-Mills theory in the Landau gauge, in the infrared regime. We argue that similar results can be obtained, in a technically simpler way, with Callan-Symanzik renormalization group equations. We present generalizations of the infrared safe renormalization scheme proposed by Tissier and Wschebor in 2011, and show how the renormalization scheme dependence can be used to improve the matching to the existing lattice data for the gluon and ghost propagators.Historically, the first semi-analytical method that has made it possible to access the deep infrared (IR) regime of Landau gauge Yang-Mills theory, have been Dyson-Schwinger equations. The first solutions of these equations that have been found show a scaling behavior of the propagators in the IR [1]. Several years later, another type of solutions of the same equations was discovered [2], with a massive gluon propagator and a finitely enhanced ghost propagator in the IR (decoupling solutions). To date, Dyson-Schwinger equations are still the main tool for the (semi-)analytical exploration of the IR regime of Yang-Mills theory.In a parallel development that actually initiated much earlier with Gribov's observation of the existence of gauge copies in his famous 1978 paper [3] and was later worked out in great detail by Zwanziger [4], the theoretical foundations of IR Yang-Mills theory in the Landau gauge were laid. While this so-called Gribov-Zwanziger scenario seemed to confirm the existence of the scaling solutions, a more recent refinement [5] favors the decoupling type of solutions. Finally, the results of simulations of Yang-Mills theory in the Landau gauge on huge lattices [6] have been interpreted by most workers in the field as confirming the realization of the decoupling type of solutions in three and four space-time dimensions.In this contribution, we will present a different technique for the exploration of the IR regime of Yang-Mills theory. We intend to reproduce the results of lattice simulations in the Landau gauge that restrict the gauge field configurations to the (first) Gribov region, but make no attempt to reach the fundamental modular region. The restriction to the Gribov region implies the breaking of BRST invariance in the continuum formulation [4]. The most important consequence of the broken BRST invariance for the IR regime is the appearance of a mass term for the gluon field [5]. Indeed, the addition of a gluonic mass term to the Yang-Mills action has been shown to reproduce all the solutions (two types of scaling solutions and the decoupling solution) found before with the help of DysonSchwinger equations when solving the Callan-Symanzik equations for this theory in the IR regime in an epsilon expansion around the upper critical space-time dimension [7]. This analysis also shows that a

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Perturbative gauge invariance: the electroweak theory

Dütsch

Schaf

1999

Ann. Phys.

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The concept of perturbative gauge invariance formulated exclusively by means of asymptotic fields is generalized to massive gauge fields. Applying it to the electroweak theory leads to a complete fixing of couplings of scalar and ghost fields and of the coupling to leptons, in agreement with the standard theory. The W/Z mass ratio is also determined, as well as the chiral character of the fermions. We start directly with massive gauge fields and leptons and, nevertheless, obtain a theory which satisfies perturbative gauge invariance.

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On a class of Lagrangian models for massive and massless Yang-mills fields

Cited by 264 publications

References 4 publications

Anti-BRST symmetry and background field method

Anti-BRST symmetry and background field method

Callan-Symanzik equations for infrared Yang-Mills theory

Perturbative gauge invariance: the electroweak theory

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