Electron-photon vertex and dynamical chiral symmetry breaking in reduced QED: An advanced study of gauge invariance

Albino, Luis; Bashir, Adnan; Mizher, Ana Júlia; Raya, Alfredo

doi:10.1103/physrevd.106.096007

Cited by 8 publications

(3 citation statements)

References 69 publications

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“…The present calculation generalizes the previously known case of QED 4 carried out in [47], motivated by the Coulomb static interaction among charge carriers in low-energy graphene. Although one usually considers graphene as a gapless system, there are a number of proposals for mechanisms which can open the gap and thus induce a mass for electrons in the material, including self interactions [24][25][26][27][28][29][30]. In this particular context, our approach is suitable for calculations.…”

Section: Discussionmentioning

confidence: 99%

“…The development of both approaches follows similar paths and consists of dimensionally reducing the gauge fields, defining an effective theory totally in (2 + 1)D that accounts for the projection of the gauge field on the plane. This procedure has been widely used to calculate chiral symmetry breaking in planar systems, mainly making use of Schwinger-Dyson techniques [26][27][28][29][30]. Renormalization in RQED was investigated in [31][32][33][34], and its scale invariance to all orders was proved in [35].…”

Section: Introductionmentioning

confidence: 99%

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Fried-Yennie Gauge in Pseudo-QED

Mizher,

Raya,

Raya

2024

Entropy

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The Fried-Yennie gauge is a covariant gauge for which the mass-shell renormalization procedure can be performed without introducing spurious infrared divergences to the theory. It is usually applied in calculations in regular Quantum Electrodynamics (QED), but it is particularly interesting when employed in the framework of pseudo-QED (PQED), where fermions are constrained to 2 + 1 dimensions while the dynamical fields interacting with these fermions live in the bulk of a 3 + 1 space. In this context, the gauge parameter can be adjusted to match the power of the external momentum in the denominator of the photon propagator, simplifying the infrared region without the need for a photon mass. In this work, we apply this machinery, for the first time, to PQED, generalizing the procedure to calculate the self energy in arbitrary dimensions, allowing, of course, for different dimensionalities of fermions and gauge fields.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fried-Yennie Gauge in Pseudo-QED

Mizher,

Raya,

Raya

2024

Entropy

Self Cite

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“…Since the seminal work by Curtis and Pennington [33], it has become evident how important the fermion-gauge-boson vertex is in achieving gauge independence in the Dyson-Schwinger approach. Although for QED substantial progress has been achieved, see, e.g., [34][35][36] and references therein, in the studies of the role of the fermion-photon vertex for gauge independence, the corresponding question in QCD, namely, on the impact of the quark-gluon vertex on the gauge (in-)dependence of hadron observables, has proven to be an extremely hard question. Even the much more humble question of how the different tensors of the quark-gluon vertex may depend on the gauge parameter within the class of linear covariant gauges and how this will effect the underlying mechanism for DχSB in this class of gauges seems beyond reach given the status of Dyson-Schwinger studies of the Yang-Mills sector in the linear covariant gauge, see, e.g., [37][38][39].…”

Section: A Note On Gauge Dependencementioning

confidence: 99%

Dynamical Chiral Symmetry Breaking in Quantum Chromo Dynamics: Delicate and Intricate

Alkofer

2023

Symmetry

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Dynamical chiral symmetry breaking (DχSB) in quantum chromo dynamics (QCD) for light quarks is an indispensable concept for understanding hadron physics, i.e., the spectrum and the structure of hadrons. In functional approaches to QCD, the respective role of the quark propagator has been evident since the seminal work of Nambu and Jona-Lasinio has been recast in terms of QCD. It not only highlights one of the most important aspects of DχSB, the dynamical generation of constituent quark masses, but also makes plausible that DχSB is a robustly occurring phenomenon in QCD. The latter impression, however, changes when higher n-point functions are taken into account. In particular, the quark–gluon vertex, i.e., the most elementary n-point function describing the full, non-perturbative quark–gluon interaction, plays a dichotomous role: It is subject to DχSB as signalled by its scalar and tensor components but it is also a driver of DχSB due to the infrared enhancement of most of its components. Herein, the relevant self-consistent mechanism is elucidated. It is pointed out that recently obtained results imply that, at least in the covariant gauge, DχSB in QCD is located close to the critical point and is thus a delicate effect. In addition, requiring a precise determination of QCD’s three-point functions, DχSB is established, in particular in view of earlier studies, by an intricate interplay of the self-consistently determined magnitude and momentum dependence of various tensorial components of the gluon–gluon and the quark–gluon interactions.

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