Four-loop singularities of the massless fermion propagator in quenched three-dimensional QED

Abstract

We calculate the three- and four-loop corrections to the massless fermion propagator in three-dimensional quenched Quantum Electrodynamics with four-component fermions. The three-loop correction is finite and gauge invariant but the four-loop one has singularities except in the Feynman gauge where it is also finite. Our results explicitly show that, up to four loops, gauge-dependent terms are completely determined by lower order ones in agreement with the Landau-Khalatnikov-Fradkin transformation.

arXiv comment11+4 pages

References in corpus (34)

• The electronic properties of graphene
• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Algebraic Fermi liquid from phase fluctuations: "topological" fermions, vortex "berryons" and QED3 theory of cuprate superconductors
• Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D
• QED3 theory of underdoped high temperature superconductors
• The Influence of the Full Vertex and Vacuum Polarization on the Fermion Propagator in QED3
• Dynamical Chiral Symmetry Breaking in Unquenched ${QED}_3$
• Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve
• The Gegenbauer Polynomial Technique: the evaluation of a class of Feynman diagrams
• Charmonium properties from lattice QCD + QED: hyperfine splitting, $J/\psi$ leptonic width, charm quark mass and $a_{\mu }^c$
• Four-loop QCD propagators and vertices with one vanishing external momentum
• Two-loop fermion self-energy in reduced quantum electrodynamics and application to the ultra-relativistic limit of graphene
• (2+1)-Dimensional QED with Dynamically Massive Fermions in the Vacuum Polarization
• Introducing SummerTime: a package for high-precision computation of sums appearing in DRA method
• Infrared cutoff dependence of the critical flavor number in three-dimensional QED
• Landau-Khalatnikov-Fradkin Transformations and the Fermion Propagator in Quantum Electrodynamics
• Gauge-theory approach to planar doped antiferromagnets and external magnetic fields
• Non-perturbative Fermion Propagator for the Massless Quenched QED3
• Does the weak coupling limit of the Burden-Tjiang deconstruction of the massless quenched QED3 vertex agree with perturbation theory?
• Numerical determination of monopole scaling dimension in parity-invariant three-dimensional non-compact QED
• Chiral symmetry breaking in dimensionally regularized nonperturbative quenched QED
• Critical behaviour of ($2+1$)-dimensional QED: 1/N_f-corrections in the Landau gauge
• Critical behaviour of ($2+1$)-dimensional QED: $1/N_f$-corrections in an arbitrary non-local gauge
• Flavor and topological current correlators in parity-invariant three-dimensional QED
• Landau-Khalatnikov-Fradkin transformation and the mystery of even $\zeta$-values in Euclidean massless correlators
• On the gauge parameter dependence of QED
• On the critical behavior of (2+1)-dimensional QED
• Landau-Khalatnikov-Fradkin transformation in three-dimensional quenched QED
• Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED
• Cutting massless four-loop propagators
• Addendum to "Critical behaviour of ($2+1$)-dimensional QED: $1/N_f$-corrections in an arbitrary non-local gauge"
• Landau-Khalatnikov-Fradkin transformation and hatted zeta-values
• Critical number of fermions in three-dimensional QED

Cited by in corpus (4)

• Critical properties of three-dimensional many-flavour QEDs
• $\mathcal{N}=1$ supersymmetric three-dimensional QED in the large-$N_f$ limit and applications to super-graphene
• Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation
• Unstable cohomology of ${\mathsf{GL}}_{2n}(\mathbb{Z})$ and the odd commutative graph complex