The nonperturbative propagator and vertex in massless quenched QED_d
  It is well known how multiplicative renormalizability of the fermion propagator, through its Schwinger-Dyson equation, imposes restrictions on the 3-point fermion-boson vertex in massless quenched quantum electrodynamics in 4-dimensions (QED$_4$). Moreover, perturbation theory serves as an excellent guide for possible nonperturbative constructions of Green functions.   We extend these ideas to arbitrary dimensions $d$. The constraint of multiplicative renormalizability of the fermion propagator is generalized to a Landau-Khalatnikov-Fradkin transformation law in $d$-dimensions and it naturally leads to a constraint on the fermion-boson vertex. We verify that this constraint is satisfied in perturbation theory at the one loop level in 3-dimensions. Based upon one loop perturbative calculation of the vertex, we find additional restrictions on its possible nonperturbative forms in arbitrary dimensions. 
A. Bashir and R. Delbourgo