  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.
