ORCID

Abstract

We study low energy photons coupled to scalar and spinor matter in the presence of an arbitrary homogeneous electromagnetic field in a first-quantized (worldline) approach. Utilizing a Fock-Schwinger gauge for both the scattering photons and homogeneous background, simple compact expressions are found for both the photon- and background-dressed effective action and propagator in scalar and spinor quantum electrodynamics. The low-energy limit allows identification of the coupling of the scattering photons as one of an effective homogeneous superposition of their field strengths, with amplitudes following from application of a suitable linearization operator. To treat the linearization, several techniques are employed, including a functional expansion based on the proper time formalism and worldline Green’s functions, linearized vertex operators under a worldline path integral, and a matrix expansion in the field strengths. We find, in particular, that a replacement rule converting scalar amplitudes to spinor amplitudes at one-loop order can, surprisingly, be extended to tree level amplitudes in the low energy limit. Finally, we discuss a novel worldline representation of the momentum space matter propagators, obtaining a suitable worldline Green’s function for this path integral satisfying homogeneous Dirichlet boundary conditions and momentum space vertex operators representing the scattering photons already in momentum space.

Publication Date

2025-11-24

Publication Title

Physical Review D

Volume

112

ISSN

2470-0010

Acceptance Date

2025-01-01

Deposit Date

2025-11-25

Funding

J. P. E. gratefully acknowledges discussion with Christian Schubert who made many insightful comments on questions of gauge dependence and light-by-light scattering. J. P. E. and P. C. are supported by EPSRC Standard Grant EP/X02413X/1. I. A. is funded by a University of Plymouth doctoral scholarship.

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