Dynamical Fermion Masses and Constraints of Gauge Invariance in Quenched QED3

Abstract

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 $\xi$ 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 $\xi$. 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 $\xi$. We also compare our results with exact numerical solutions available for a small number of values of $\xi$ obtained through a direct analysis of the corresponding SDE.

10 pages, 8 figures, uses Revtex4

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• Chiral Symmetry Breaking and Confinement Beyond Rainbow-Ladder Truncation
• Massive Dirac fermions and the zero field quantum Hall effect
• Finite volume effects and dynamical chiral symmetry breaking in QED3
• Multiple solutions for the fermion mass function in QED3
• 3-point off-shell vertex in scalar QED in arbitrary gauge and dimension
• Implications of analyticity to solution of Schwinger-Dyson equations in Minkowski space
• The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking
• Critical Number of Flavours in QED
• Gauge dependence of the quark gap equation: an exploratory study
• Gauge Covariance Relations and the Fermion Propagator in Maxwell-Chern-Simons QED3
• Vacuum Polarization and Dynamical Chiral Symmetry Breaking: Phase Diagram of QED with Four-Fermion Contact Interaction
• Constructing Scalar-Photon Three Point Vertex in Massless Quenched Scalar QED
• Electron-Photon Vertex and Dynamical Chiral Symmetry Breaking in Reduced QED: An Advanced Study of Gauge Invariance
• QED3 at Finite Temperature and Density
• Unconventional behavior of Dirac fermions in three-dimensional gauge theory
• Landau-Khalatnikov-Fradkin Transformations, Nielsen Identities, Their Equivalence and Implications for QCD
• Instability in scalar channel of fermion-antifermion scattering amplitude in massless QED_3 and anomalous dimensions of composite operators
• Gauge dependence of the infrared behaviour of massless QED_3
• Gauge covariance of the gap equation: from the rainbow truncation to gauge symmetry constraints
• Planar generalized electrodynamics for one-loop amplitude in the Heisenberg picture