Landau-Khalatnikov-Fradkin transformations in reduced quantum electrodynamics

Ahmad, Aftab; Cobos-Martínez, J. J.; Concha‐Sánchez, Y.; Raya, Alfredo

doi:10.1103/physrevd.93.094035

Cited by 31 publications

(47 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, we have verified that the bare results for Σ 1V (ξ) and Σ 2bcV (ξ) are exactly in agreement with the LKF transformation (using dimensional regularization, our derivations proceed without any replacements involving a cut-off parameter Λ and the scale µ as in the case of Ref. [12]).…”

Section: B Lkf Transformationsupporting

confidence: 75%

Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED

2020

View full text Add to dashboard Cite

We study the gauge-covariance of the massless fermion propagator in reduced Quantum Electrodynamics (QED). Starting from its value in some gauge, we evaluate an all order expression for it in another gauge by means of the Landau-Khalatnikov-Fradkin (LKF) transformation. We find that the weak coupling expansions thus derived are in perfect agreement with the exact calculations. We also prove that the fermion anomalous dimension of reduced QED is gauge invariant to all orders of perturbation theory except for the first one.

show abstract

Section: B Lkf Transformationsupporting

confidence: 75%

Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED

2020

View full text Add to dashboard Cite

show abstract

“…Starting with a perturbative propagator in some fixed gauge, say η, all the coefficients depending on the difference between the gauge fixing parameters of the two propagators, ξ − η, get fixed by a weak coupling expansion of the LKF-transformed initial one. Such estimations have been carried out for QED in various dimensions (see [9,10]), for generalizations to brane worlds [11] and for more general SU(N) gauge theories [12].…”

Section: Introductionmentioning

confidence: 99%

Landau-Khalatnikov-Fradkin transformation and the mystery of even ζ -values in Euclidean massless correlators

Kotikov

Teber

2019

Phys. Rev. D

View full text Add to dashboard Cite

The Landau-Khalatnikov-Fradkin (LKF) transformation is a powerful and elegant transformation allowing to study the gauge dependence of the propagator of charged particles interacting with gauge fields. With the help of this transformation, we derive a non-perturbative identity between massless propagators in two different gauges. From this identity, we find that the corresponding perturbative series can be exactly expressed in terms of a hatted transcendental basis that eliminates all even Euler ζ-functions. This explains the mystery of even ζ-values observed in multi-loop calculations of Euclidean massless correlators for almost three decades now. Our construction further allows us to derive an exact formula relating hatted and standard ζ-functions to all orders of perturbation theory.

show abstract

“…In the last years, there has been an increasing number of studies focusing on reduced QED and in particular QED 4,3 in relation with, e.g., transport and spectral properties [26][27][28][29], see also the short review [30], optical properties [31,32], quantum Hall effect [20,33,34] and dynamical chiral symmetry breaking [35,36] in planar systems. Moreover, QED 4,3 was shown to be unitary [37], its properties under the Landau-Khalatnikov-Frandkin transformation were studied [38], its precise relation to QED 3 understood [35], it was shown to possess a strong-weak duality mapping the coupling constant e toẽ = 8π/e with a self-dual point at e 2 = 8π (or α = 2) [39] and, even more recently, it has been studied as an interacting boundary conformal field theory [40].…”

Section: Introductionmentioning

confidence: 99%

Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultrarelativistic limit of Dirac liquids

Teber

Kotikov

2018

Phys. Rev. D

View full text Add to dashboard Cite

The field theoretic renormalization study of reduced quantum electrodynamics (QED) is performed up to two loops. In the condensed matter context, reduced QED constitutes a very natural effective relativistic field theory describing (planar) Dirac liquids, e.g., graphene and graphenelike materials, the surface states of some topological insulators, and possibly half-filled fractional quantum Hall systems. From the field theory point of view, the model involves an effective (reduced) gauge field propagating with a fractional power of the d'Alembertian in marked contrast with usual QEDs. The use of the Bogoliubov-ParasiukHepp-Zimmermann prescription allows for a simple and clear understanding of the structure of the model. In particular, in relation with the ultrarelativistic limit of graphene, we straightforwardly recover the results for both the interaction correction to the optical conductivity C Ã ¼ ð92 − 9π 2 Þ=ð18πÞ and the anomalous dimension of the fermion field γ ψ ðᾱ; ξÞ ¼ 2ᾱð1 − 3ξÞ=3 − 16ðζ 2 N F þ 4=27Þᾱ 2 þ Oðᾱ 3 Þ, whereᾱ ¼ e 2 =ð4πÞ 2 and ξ is the gauge-fixing parameter.

show abstract

Landau-Khalatnikov-Fradkin transformations in reduced quantum electrodynamics

Cited by 31 publications

References 59 publications

Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED

Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED

Landau-Khalatnikov-Fradkin transformation and the mystery of even ζ -values in Euclidean massless correlators

Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultrarelativistic limit of Dirac liquids

Contact Info

Product

Resources

About