Gauge covariant solution for the Schwinger-Dyson equation in   three-dimensional QED with Chern-Simons term
  An Abelian gauge theory with Chern-Simons term is investigated for a four-component Dirac fermion in 1+2 dimensions. The Ball-Chiu (BC) vertex function is employed to modify the rainbow-ladder approximation for the Schwinger-Dyson (SD) equation. We numerically solve the SD equation and show the gauge dependence for the resulting phase boundary for the parity and the chiral symmetry. 
Yuichi Hoshino, Tomohiro Inagaki and Yuichi Mizutani
hep-ph hep-th