# On elastic scattering amplitude of planar charged fermions in a constant magnetic field

## TL;DR

This paper calculates the elastic scattering amplitude of charged fermions in 2+1D QED under a constant magnetic field, analyzing both massive and massless cases, and relates the imaginary part to photon emission probabilities.

## Contribution

It provides the first detailed calculation of ESA in 2+1D QED with an external magnetic field, including the massless limit and high Landau level approximations.

## Key findings

- Analytical formulas for ESA at high Landau levels
- Relation between ESA imaginary part and photon emission probability
- Explicit expressions for massive and massless fermion cases

## Abstract

The elastic scattering amplitude (ESA) is obtained in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED$_{2+1}$) for planar charged fermions in an external constant magnetic field. We obtain the elastic scattering amplitude in the corresponding massive theory and then discuss and calculate the massless limit of ESA. The imaginary part of ESA are related to the total probability of photons emission by charged fermions in the considered magnetic field. Simple analytical formulas are obtained when planar charged fermions in initial states occupy high excited Landau levels.