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An Abelian gauge theory with Chern-Simons term is investigated for afour-component Dirac fermion in 1+2 dimensions. The Ball-Chiu (BC) vertexfunction is employed to modify the rainbow-ladder approximation for theSchwinger-Dyson (SD) equation. We numerically solve the SD equation and showthe gauge dependence for the resulting phase boundary for the parity and thechiral symmetry.

Gauge covariant solution for the Schwinger-Dyson equation in three-dimensional QED with Chern-Simons term