Analytic Form of the One-loop Vertex and of the Two-loop Fermion Propagator in 3-Dimensional Massless QED

Abstract

We evaluate the analytic expression for the one-loop fermion-boson vertex in massless QED3 in an arbitrary covariant gauge. The result is written in terms of elementary functions of its momenta. The vertex is decomposed into a longitudinal part, that is fully responsible for ensuring the Ward and Ward-Takahashi identities are satisfied, and a transverse part. Following Ball and Chiu and Kızılersü {\it et. al.}, the transverse part is written in its most general form as a function of 4 independent vectors. We calculate the coefficients of each of these vectors. We also check the transversality condition to two loops and evaluate the fermion propagator to the same order. We compare our results with a conjecture of the non-perturbative vertex by Tjiang and Burden.

arXiv comment22 pages, Latex, 2 Postscript figures

Cited by in corpus (11)

• Dyson-Schwinger Equations: Density, Temperature and Continuum Strong QCD
• Landau-Khalatnikov-Fradkin Transformations and the Fermion Propagator in Quantum Electrodynamics
• Chiral Symmetry Breaking and Confinement Beyond Rainbow-Ladder Truncation
• Local Gauge Transformation for the Quark Propagator in an SU(N) Gauge Theory
• Neutron electric dipole moment: Constituent-dressing and compositeness
• Effect of the Quark-Gluon Vertex on Dynamical Chiral Symmetry Breaking
• The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking
• Continuum Strong QCD: Confinement and Dynamical Chiral Symmetry Breaking
• Gauge Symmetry and its Implications for the Schwinger-Dyson Equations
• Non-perturbative gauge transformations of arbitrary fermion correlation functions in quantum electrodynamics
• Non-perturbative Aspects of Schwinger-Dyson Equations