Running Coupling Constant of a Gauge Theory in the Framework of the   Schwinger-Dyson Equation: Infrared Behavior of Three-Dimensional Quantum   Electrodynamics
  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. 
Kei-Ichi Kondo (Chiba/Oxford University)