S-Matrix approach to Compton scattering at the tree level in a strong magnetic field

TL;DR

This paper investigates Compton scattering in a strong magnetic field using the S-matrix approach, revealing that the magnetic field decreases the cross section compared to vacuum but causes it to increase linearly with field strength.

Contribution

It provides a detailed calculation of Compton scattering cross section in a strong magnetic field at the tree level using the Schwinger propagator and Landau level approximation.

Findings

Cross section decreases in strong magnetic fields compared to vacuum.

For fixed photon energy, cross section increases linearly with magnetic field strength.

Analysis is performed at the lowest Landau level in the strong field regime.

Abstract

We have studied the Compton scattering ($\gamma e^- \longrightarrow \gamma e^-$) at the tree level in a homogeneous background of strong magnetic field ($|eB| \gg { m }^{ 2 },~\text{m is the mass of electron}$) through the S-matrix approach. For that purpose, using the Schwinger propagator for the electron, we have first calculated the square of the S-matrix element in the Landau gauge by summing over the final states of electron and photon and averaging over the initial states of the same. In the strong magnetic field, only the lowest Landau level for electron is considered. Finally we have computed the crosssection for Compton scattering as a function of initial photon energy for the different strengths of strong magnetic fields, where we have found that the crosssection in vacuum gets decreased due to the presence of strong magnetic field. However, for a fixed initial photon energy, the crosssection increases linearly with the magnetic field.