Generalized two-point tree-level amplitude $jf \to j^{\, \prime} f^{\, \prime}$ in a magnetized medium (extended version)

TL;DR

This paper derives and analyzes the tree-level two-point amplitudes for fermion-current interactions in a magnetized medium, covering various interaction types and magnetic field strengths, including special cases like strong fields and forward scattering.

Contribution

It extends the calculation of two-point amplitudes to arbitrary magnetic field strengths and various interaction vertices, including special cases like strong fields and forward scattering.

Findings

Derived general expressions for two-point amplitudes in a magnetic field.

Analyzed special cases such as strong magnetic fields and forward scattering.

Provided insights into fermion-current interactions in magnetized media.

Abstract

The tree-level two-point amplitudes for the transitions $jf \to j^{\, \prime} f^{\, \prime}$, where $f$ is a fermion and $j$ is a generalized current, in a constant uniform magnetic field of an arbitrary strength and in charged fermion plasma, for the $jf$ interaction vertices of the scalar, pseudoscalar, vector and axial-vector types have been investigated. The particular cases of a very strong magnetic field, and of the coherent scattering off the real fermions without change of their states (the "forward" scattering) have been analysed.