Landau-Khalatnikov-Fradkin transformations and the fermion propagator in quantum electrodynamics

Bashir, Adnan; Raya, Alfredo

doi:10.1103/physrevd.66.105005

Cited by 62 publications

(88 citation statements)

References 41 publications

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“…Such an investigation, however, is hampered by the fact that the transformation law for the vertex is quite complicated. Therefore an indirect strategy has been applied: one calculates the propagator with a given vertex ansatz in the fermion and photon DSE in various gauges and compares with the corresponding results from the LKFT of the propagator [24,31,34,35]. The success of this strategy has been limited by the problem that the LKFT is formulated in coordinate space and the necessary Fourier-transform can be carried out analytically only for very special cases.…”

Section: Introductionmentioning

confidence: 99%

Dynamical chiral symmetry breaking in unquenchedQED3

et al. 2004

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We investigate dynamical chiral symmetry breaking in unquenched QED 3 using the coupled set of Dyson-Schwinger equations for the fermion and photon propagators. For the fermion-photon interaction we employ an ansatz which satisfies its Ward-Green-Takahashi identity. We present self-consistent analytical solutions in the infrared as well as numerical results for all momenta. In Landau gauge, we find a phase transition at a critical number of flavours of N crit f ≈ 4. In the chirally symmetric phase the infrared behaviour of the propagators is described by power laws with interrelated exponents. For N f = 1 and N f = 2 we find small values for the chiral condensate in accordance with bounds from recent lattice calculations. We investigate the Dyson-Schwinger equations in other linear covariant gauges as well. A comparison of their solutions to the accordingly transformed Landau gauge solutions shows that the quenched solutions are approximately gauge covariant, but reveals a significant amount of violation of gauge covariance for the unquenched solutions.

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Section: Introductionmentioning

confidence: 99%

Dynamical chiral symmetry breaking in unquenchedQED3

et al. 2004

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“…where and note that it obviously reduces to (8) and (48) on setting ξ = 0. We separate the discussion on the bare and the full vertex in the following subsections.…”

Section: Numerical Findingsmentioning

confidence: 99%

“…Momentum space calculations are more tedious, owing to the complications induced by Fourier transforms. These difficulties are reflected in [8] where non perturbative FP is obtained starting from a perturbative one in the Landau gauge in QED3 and QED4.…”

Section: Introductionmentioning

confidence: 99%

Dynamical fermion masses and constraints of gauge invariance in quenched QED3

Bashir

Raya

2005

Nuclear Physics B

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Numerical study of the Schwinger-Dyson equation (SDE) for the fermion propagator (FP) to obtain dynamically generated chirally asymmetric solution in an arbitrary covariant gauge ξ is a complicated exercise specially if one employs a sophisticated form of the fermion-boson interaction complying with the key features of a gauge field theory. However, constraints of gauge invariance can help construct such a solution without having the need to solve the Schwinger-Dyson equation for every value of ξ. In this article, we propose and implement a method to carry out this task in quenched quantum electrodynamics in a plane (QED3). We start from an approximate analytical form of the solution of the SDE for the FP in the Landau gauge. We consider the cases in which the interaction vertex (i) is bare and (ii) is full. We then apply the Landau-Khalatnikov-Fradkin transformations (LKFT) on the dynamically generated solution and find analytical results for arbitrary value of ξ. We also compare our results with exact numerical solutions available for a small number of values of ξ obtained through a direct analysis of the corresponding SDE.

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“…They can not only be used to change from one covariant gauge to another at a fixed loop level, but also to predict higher-loop terms from lower-loop ones. However, those predicted terms will all be gauge parameter dependent [10][11][12][13]. There have been many efforts to construct the three -point vertex in a way that would ensure the LKFT law for the massless fermion propagator, see, for example, [10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Multiphoton Amplitudes and Generalized LKF Transformation in Scalar QED Using the Worldline Formalism

2017

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We apply the worldline formalism to scalar quantum electrodynamics (QED) to find a BernKosower type master formula for generalized Compton scattering, on-shell and off-shell. Moreover, we use it to study the non-perturbative gauge parameter dependence of amplitudes in scalar QED and, as our main result, find a simple non-perturbative transformation rule under changes of this parameter in x-space in terms of conformal cross ratios. This generalizes the well-known Landau-Khalatnikov-Fradkin transformation (LKFT). We also exemplify how the LKFT works in perturbation theory.

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Landau-Khalatnikov-Fradkin transformations and the fermion propagator in quantum electrodynamics

Cited by 62 publications

References 41 publications

Dynamical chiral symmetry breaking in unquenchedQED3

Dynamical chiral symmetry breaking in unquenchedQED3

Dynamical fermion masses and constraints of gauge invariance in quenched QED3

Multiphoton Amplitudes and Generalized LKF Transformation in Scalar QED Using the Worldline Formalism

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