We study the gauge covariance of the fermion propagator in Maxwell–Chern–Simons planar quantum electrodynamics (QED3) considering four-component spinors with parity-even and parity-odd mass terms for both fermions and photons. Starting with its tree-level expression in the Landau gauge, we derive a non-perturbative expression for this propagator in an arbitrary covariant gauge by means of its Landau–Khalatnikov–Fradkin transformation (LKFT). We compare our findings in the weak coupling regime with the direct one-loop calculation of the two-point Green function and observe perfect agreement up to a gauge-independent term. We also reproduce results derived in earlier works as special cases of our findings.

We study the analytical structure of the fermion propagator in planar quantum electrodynamics coupled to a Chern-Simons term within a four-component spinor formalism. The dynamical generation of parity-preserving and parity-violating fermion mass terms is considered, through the solution of the corresponding Schwinger-Dyson equation for the fermion propagator at leading order of the 1/N approximation in Landau gauge. The theory undergoes a first order phase transition toward chiral symmetry restoration when the Chern-Simons coefficient θ reaches a critical value which depends upon the number of fermion families considered. Parity-violating masses, however, are generated for arbitrarily large values of the said coefficient. On the confinement scenario, complete charge screening -characteristic of the 1/N approximation-is observed in the entire (N, θ)-plane through the local and global properties of the vector part of the fermion propagator.

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