Dynamical fermion masses and constraints of gauge invariance in quenched QED3

Bashir, Adnan; Raya, Alfredo

doi:10.1016/j.nuclphysb.2004.12.010

Cited by 40 publications

(29 citation statements)

References 34 publications

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“…The problem originates from the fact that the SDEs are built out of unphysical Green's functions; thus, the extraction of reliable physical information depends critically on the delicate all-order cancellations we have been describing in this review, which may be inadvertently distorted in the process of the truncation. For example, several of the issues related to the truncation of the SDEs of QED have been addressed in [171][172][173][174][175][176][177][178][179][180]; it goes without saying that the situation becomes even more complicated for strongly coupled non-Abelian gauge theories, such as QCD [181], mainly because of the following two reasons.…”

Section: Sdes For Non-abelian Gauge Theories: Difficulties With the Cmentioning

confidence: 99%

Pinch technique: Theory and applications

2009

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We review the theoretical foundations and the most important physical applications of the Pinch Technique (PT). This general method allows the construction of off-shell Green's functions in non-Abelian gauge theories that are independent of the gauge-fixing parameter and satisfy ghost-free Ward identities. We first present the diagrammatic formulation of the technique in QCD, deriving at one loop the gauge independent gluon self-energy, quark-gluon vertex, and three-gluon vertex, together with their Abelian Ward identities. The generalization of the PT to theories with spontaneous symmetry breaking is carried out in detail, and the profound connection with the optical theorem and the dispersion relations are explained within the electroweak sector of the Standard Model. The equivalence between the PT and the Feynman gauge of the Background Field Method (BFM) is elaborated, and the crucial differences between the two methods are critically scrutinized. A variety of field theoretic techniques needed for the generalization of the PT to all orders are introduced, with particular emphasis on the Batalin-Vilkovisky quantization method and the general formalism of algebraic renormalization. The main conceptual and technical issues related to the extension of the technique beyond one loop are described, using the twoloop construction as a concrete example. Then the all-order generalization is thoroughly examined, making extensive use of the field theoretic machinery previously introduced; of central importance in this analysis is the demonstration that the PT-BFM correspondence persists to all orders in perturbation theory. The extension of the PT to the non-perturbative domain of the QCD Schwinger-Dyson equations is presented systematically, and the main advantages of the resulting self-consistent truncation scheme are discussed. A plethora of physical applications relying on the PT are finally reviewed, with special emphasis on the definition of gauge-independent off-shell form-factors, the construction of non-Abelian effective charges, the gauge-invariant treatment of resonant transition amplitudes and unstable particles, and finally the dynamical generation of an effective gluon mass.

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Section: Sdes For Non-abelian Gauge Theories: Difficulties With the Cmentioning

confidence: 99%

Pinch technique: Theory and applications

2009

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“…It is essential to apply LKFT to the dynamically generated mass function as advocated in [11,12]. This is what we achieve in an exact numerical fashion.…”

Section: Discussionmentioning

confidence: 91%

“…These are non-perturbative in nature, and thus are expected to be very helpful in studies of phenomena realized only non perturbatively, such as dynamical chiral symmetry breaking. Initial steps were taken in [12] to apply LKFT directly to the dynamically generated mass function, whereas the complete numerical implementation of LKFTs on solutions to SDEs in various truncation schemes was performed in [11] to study the gauge dependence of the chiral condensate in QED3. In this work we extend the analysis to a wider range of values of the gauge parameter.…”

Section: Introductionmentioning

confidence: 99%

Gauge Covariance and the Chiral Condenate in QED3

Bashir¹,

Raya²

2007

Braz. J. Phys.

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The ambiguities associated with the lack of gauge invariance in the non-perturbative truncations of Schwinger-Dyson equations (SDEs) are a challenging problem which has not yet been resolved in a decisive fashion. Pursuing this aim, we study dynamical chiral symmetry breaking in quantum electrodynamics in three space-time dimensions (QED3). We investigate the gauge dependence of the chiral condensate both in the quenched and the unquenched versions of the theory and emphasize the importance of taking into account the gauge covariance properties of the fermion propagator as dictated by its Landau-Khalatnikov-Fradkin transformation (LKFT). We present numerical solutions of the SDE of the fermion propagator which respect Ward-Green-Takahashi identities (WGTI) and LKFT simultaneously. As a striking consequence, we obtain a practically gauge independent chiral condensate.

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“…It is essential to apply LKFT to the dynamically generated mass function as advocated in [21]. This is what we achieve in this letter in an exact numerical fashion.…”

mentioning

confidence: 76%

“…As LKFT are non-perturbative in nature, we expect them not only to be satisfied at every order in perturbation theory but also in phenomena which are realized non perturbatively, such as dynamical chiral symmetry breaking. Initial steps were taken in [21] to apply these transformations directly to the dynamically generated mass function. As a continuation of this effort, here we carry out an exact numerical exercise to study the gauge dependence of the chiral condensate in QED3.…”

mentioning

confidence: 99%