Screening length in (2+1)-dimensional Abelian Chern–Simons theories

V.S Alves,Ashok Das,Silvana Perez

doi:10.1016/s0370-2693(02)01486-7

Abstract

Abstract In this Letter, we systematically study the question of screening length in Abelian Chern–Simons theories. In the Abelian Higgs theory, where there are two massive poles in the gauge propagator at the tree level, we show that the coefficient of one of them becomes negligible at high temperature and that the screening length is dominantly determined by the parity violating part of the self-energy. In this theory, static magnetic fields are screened. In the fermion theory, on the other hand, the parity conserving part of the self-energy determines the screening length and static magnetic fields are not screened. Several other interesting features are also discussed.

Highlights

The properties of a charged plasma, at finite temperature, have been studied extensively in the past in 3 + 1 dimensions [1, 2, 3, 4] and it is known that there are several interesting features that emerge in thermal QED
The screening length between two static charges is related to the electric mass of the photon, mel, while the length associated with plasma oscillations due to a sudden excitation of the plasma is related to the plasmon mass, mpl, and the two masses are quite distinct
Our calculations are completely consistent with the known results about loop diagrams with distinct masses in that the photon self-energy is analytic in the lowest order [17, 18]

Summary

Introduction

The properties of a charged plasma, at finite temperature, have been studied extensively in the past in 3 + 1 dimensions [1, 2, 3, 4] and it is known that there are several interesting features that emerge in thermal QED. In a 2 + 1 dimensional Abelian Higgs model with a Chern-Simons term [9, 10, 11, 12], it is known that even the tree level gauge boson propagator has two distinct poles. This raises the interesting question, namely, whether there is a unique screening length in such theories. We note here that the question of screening length, in a Yang-Mills-Chern-Simons theory interacting with fermions, has been discussed in the past [13] and we compare our results with these

Abelian Higgs model with a Chern-Simons term

T and the Boltzmann constant k

The calculations

Static Limit

Long Wave Limit

Discussion of results