4 v 3 6 N ov 1 99 6 The effective electromagnetic interaction in a dense fermionic medium in QED 2 +

The effective electromagnetic interaction in a dense fermionic medium in QED 2+1. Abstract The effective Lagrangian of arbitrary varying in space electromagnetic field in a dense medium is derived. It has been used for investigation of interaction between charged fermions in the medium. It is shown the possibility for the formation of metastable electron bound states in the medium when external magnetic field is applied. 1 Introduction The method of effective Lagrangians has been well developed for the cases of homogeneous [1] and/or smoothly varying [2] external fields. However, in some problems, for example, such as photon splitting in the electron-positron plasma [3] it is necessary to consider gauge fields rapidly varying in space or time. For such a type of conditions the calculation of the effective Lagrangian (EL) is not trivial. In the paper [4] some important properties and the dependence on chemical potential µ of the polarization tensor and the three-photonic vertex in a dense medium were discovered. The results obtained allow to construct EL for arbitrary inhomogeneous static electromagnetic fields. The goal of the present paper is to obtain EL of electromagnetic field in a dense fermionic medium by making use the discovered properties of polarization tensors and investigate the corresponding interaction of charged fermions in a dense environment. Although proposed procedure has a general character and is expected to be applicable for various gauge theories, here we shall consider two-dimensional quantum electrodynamics which is widely used for investigation of high temperature superconductivity [5] and quantum Hall effect [6].