Off-shell Green functions at one-loop level in Maxwell-Chern-Simons quantum electrodynamics

Abstract

We derive the off-shell photon propagator and fermion-photon vertex at one-loop level in Maxwell-Chern-Simons quantum electrodynamics in arbitrary covariant gauge, using fourcomponent spinors with parity-even and parity-odd mass terms for both fermions and photons.We present our results using a basis of two, three and four point integrals, some of them not known previously in the literature. These integrals are evaluated in arbitrary space-time dimensions so that we reproduce results derived earlier under certain limits.

Gauge-covariant solution for the Schwinger-Dyson equation in 3D QED with a Chern-Simons term

“…It is expected that the gauge dependence is suppressed in the solution of Eqs. (16) and (21) compared with the rainbow-ladder approximation. At the limit µ → 0, the right-hand side of Eqs.…”

“…At the limit µ → 0, the right-hand side of Eqs. (16) and (21) have equivalent forms for each parities and independent on the sign for B ± . Thus we find the solutions,…”

“…(5) or eliminating terms proportional to B(p) − B(k) in Eqs. (16) and (21), we obtain the following simpler simultaneous equations:…”

“…The k-integration in Eqs. (16), (21), (29) and (34) is performed by using the trapezoidal rule from Λ IR to Λ U V . Since a non-trivial behavior is observed for B ± (p) at low momentum, we want to sample low momentum interval more frequently and reduce the numerical cost.…”

Electro- and magnetostatics of topological insulators as modeled by planar, spherical, and cylindricalθboundaries: Green’s function approach

“…In other contexts, θ ED under consideration here has been studied as a 3 þ 1 particular kind of Maxwell-Chern-Simons electrodynamics, where it has received considerable attention [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. And also it has been studied as a restricted subset of the Standard Model extension [32,33], where several results have been achieved, too [34][35][36][37][38][39][40].…”