Multiphoton amplitude in a constant background field

¹ Department of Physics, Gomal University, 29220 D.I. Khan, K.P.K., Pakistan.
² Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo. Edificio C-3, Ciudad Universitaria, Morelia 58040 Michoacán, México.
³ Center for Relativistic Laser Science, Institute for Basic Science, Gwangju 61005, Korea.
⁴ Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Universitá di Modena e Reggio Emilia, Via Campi 213/A, I-41125 Modena, Italy.
⁵ INFN, Sezione di Bologna, Via Irnerio 46, I-40126 Bologna, Italy.
⁶ Department of Physics, Kunsan National University, Kunsan 54150, Korea.

^* e-mail: aftab.gu@gmail.com
^** e-mail: ahmadiniaz@ibs.re.kr (speaker)
^*** e-mail: olindo.corradini@unimore.it
^**** e-mail: sangkim@kunsan.ac.kr
^† e-mail: schubert@ifm.umich.mx

Published online: 9 January 2018

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.