Gauge Covariance and the Chiral Condenate in QED3

Bashir, Adnan; Raya, Alfredo

doi:10.1590/s0103-97332007000200024

Cited by 8 publications

(7 citation statements)

References 18 publications

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“…( 35) together with ( 36) and (37) on the other hand. Moreover, for the coefficients âm (ξ, p) in the transformation (35), we managed to obtain the closed expression (41) in terms of the generalized Wright function 1 Ψ 1 whose asymptotic expansion gives Eqs. ( 36) and (37).…”

Section: Discussionmentioning

confidence: 99%

“…The transformation (35), which is similar to the ones used at lower orders in other papers [35,[39][40][41], allowed us to study the gauge-evolution (from the η-gauge to the ξ-gauge) of each initial magnitude a m (η) and to reproduce all results of the previous studies [35,39].…”

Section: Discussionmentioning

confidence: 99%

“…Because of this finiteness, it is tempting to set ε = 0 in Eq. (41). We consider this possibility here as a prerequisite to the more complete analysis of the following (sub-)sections.…”

Section: P-space Analysismentioning

confidence: 99%

“…However, in momentum space, the LKF transformations have a rather complicated form for the vertex, and this is the reason why they were not fully involved yet for restricting the form of the vertex even in the quenched approximation (for work in this direction, see papers by Bashir and collaborators [35,39,40] and the review in Ref. [41]).…”

Section: Introductionmentioning

confidence: 99%

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Landau-Khalatnikov-Fradkin transformation in three-dimensional quenched QED

Gusynin,

Kotikov,

Teber

2020

Preprint

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We study the gauge-covariance of the massless fermion propagator in three-dimensional quenched Quantum Electrodynamics in the framework of dimensional regularization in d = 3 − 2ε. Assuming the finiteness of the quenched perturbative expansion, that is the existence of the limit ε → 0, we state that, exactly in d = 3, all odd perturbative coefficients, starting with the third order one, should be zero in any gauge.1 At the next-to-leading order of the 1/N -expansion, the polarization operator reads: Π(q 2 ) = N Ce 2 /(8q) where C = 1 + (184/9π 2 − 2)/N . This result was obtained independently and by different methods in Refs. [12][13][14]. At the interacting IR fixed point, the beta function therefore retains the form (3) with N → N C. This in turn implies that the IR fixed point remains stable as it is only weakly affected by next-to-leading order corrections: α → 8/(N C) ≈ (8/N )(1 − 0.071/N ), in agreement with Eq. ( 30) of [13]. To the best of our knowledge, calculations at the order 1/N 3 have not been performed yet.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…Because of this finiteness, it is tempting to set ε = 0 in Eq. (41). We consider this possibility here as a prerequisite to the more complete analysis of the following (sub-)sections.…”

Section: P-space Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Landau-Khalatnikov-Fradkin transformation in three-dimensional quenched QED

Gusynin,

Kotikov,

Teber

2020

Preprint

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“…Such constraints have been studied in some detail in [2,3,4]. In the momentum space, these transformations translate as [5,6].…”

Section: Gauge Covariance Of the Fermion Propagatormentioning

confidence: 99%

Gauge-invariant masses through Schwinger-Dyson equations

Bashir¹,

Raya²

2007

AIP Conference Proceedings

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Schwinger-Dyson equations (SDEs) are an ideal framework to study non-perturbative phenomena such as dynamical chiral symmetry breaking (DCSB). A reliable truncation of these equations leading to gauge invariant results is a challenging problem. Constraints imposed by Landau-Khalatnikov-Fradkin transformations (LKFT) can play an important role in the hunt for physically acceptable truncations. We present these constrains in the context of dynamical mass generation in QED in 2 + 1-dimensions.

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