Multiphoton amplitude in a constant background field

Aftab Ahmad,Olindo Corradini,Christian Schubert,Naser Ahmadiniaz,Sang Pyo Kim,B Gwak,C Kim,C.-H Lee,H.-C Kim,W Lee,S Lee,J Lee,G Kang

doi:10.1051/epjconf/201816804003

Abstract

In this contribution, we present our recent compact master formulas for the multiphoton amplitudes of a scalar propagator in a constant background field using the worldline fomulation of quantum field theory. The constant field has been included nonperturbatively, which is crucial for strong external fields. A possible application is the scattering of photons by electrons in a strong magnetic field, a process that has been a subject of great interest since the discovery of astrophysical objects like radio pulsars, which provide evidence that magnetic fields of the order of 1012G are present in nature. The presence of a strong external field leads to a strong deviation from the classical scattering amplitudes. We explicitly work out the Compton scattering amplitude in a magnetic field, which is a process of potential relevance for astrophysics. Our final result is compact and suitable for numerical integration.

Highlights

The “worldline” or “Feynman-Schwinger” [1] representation of the one-loop effective action in scalar QED isΓ[A] = − ∞ dT e−m2T Dx(τ) e−
This Green’s function follows the SI boundary conditions. This master formula, and its extension to spinor QED [5, 10], are generally more efficient for constant field calculations in QED than the standard method based on Feynman diagrams
In the previous section we have presented a master formula for an open line in vacuum, in the following we consider a constant external field to be included in this master formula

Summary

Introduction

The “worldline” or “Feynman-Schwinger” [1] representation of the one-loop effective action in scalar QED is. This Green’s function follows the SI boundary conditions This master formula, and its extension to spinor QED [5, 10], are generally more efficient for constant field calculations in QED than the standard method based on Feynman diagrams. In 1996 Daikouji et al [13] obtained the following “Bern-Kosower type” master formula for the N-photon dressed scalar propagator in vacuum (see [14] for a recent rederivation): Dpp (k1, ε1; · · · ; kN, εN) = (−ie)N(2π)DδD p + p + ki i=1.

Free propagator

Dressed propagator

Compton scattering in a constant field

Summary