  We discuss how to define and obtain the running coupling of a gauge theory in
the approach of the Schwinger-Dyson equation, in order to perform a
non-perturbative study of the theory. For this purpose, we introduce the
nonlocally generalized gauge fixing into the SD equation, which is used to
define the running coupling constant (this method is applicable only to a gauge
theory). Some advantages and validity of this approach are exemplified in QED3.
This confirms the slowing down of the rate of decrease of the running coupling
and the existence of non-trivial infra-red fixed point (in the normal phase) of
QED3, claimed recently by Aitchison and Mavromatos, without so many of their
approximations. We also argue that the conventional approach is recovered by
applying the (inverse) Landau-Khalatnikov transformation to the nonlocal gauge
result.
