Running Coupling Constant of a Gauge Theory in the Framework of the Schwinger-Dyson Equation: Infrared Behavior of Three-Dimensional Quantum Electrodynamics

Abstract

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.

27 pages (latex) + two eps figures

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Cited by in corpus (7)

• Effect of gauge boson mass on chiral symmetry breaking in QED${}_3$
• Transverse Ward-Takahashi Identity, Anomaly and Schwinger-Dyson Equation
• Deconstructing the vertex Ansatz in three dimensional quantum electrodynamics
• Non-linear Dynamics in QED_3 and Non-trivial Infrared Structure
• Matter fields near quantum critical point in (2+1)-dimensional U(1) gauge theory
• A condition on the chiral symmetry breaking solution of the Dyson-Schwinger equation in three-dimensional QED
• Non-perturbative solutions of the SD equation for an Abelian gauge field theory