Coupling of Electromagnetic and Statistical Interactions for Two-Dimensional Electrons.

We study a nonlocal theory that describes both the electromagnetic and statistical interactions among two-dimensional electrons. This is shown through the effective action of the model. While the electromagnetic interaction is described by the so-called Pseudo Quantum Electrodynamics (PQED), the statistical part is obtained from the well-known Chern-Simons action. In the static limit, we show that the Chern-Simons parameter plays the role of an effective dielectric constant, which decreases the interaction in the large-screening limit. Thereafter, we apply the one-loop perturbation theory in our model. Within this approach, we calculate the electron self-energy, the electron renormalized mass, the corrected gauge-field propagator, and the renormalized Fermi velocity for both high- and low-speed limits, using the renormalization group.