Low-energy multi-photon scattering at tree-level and one-loop order in a homogeneous electromagnetic field
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arXiv
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| Formato: | Preprint |
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2025
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| _version_ | 1866909932896387072 |
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| author | Ahumada, Ivan Copinger, Patrick Edwards, James P. |
| author_facet | Ahumada, Ivan Copinger, Patrick Edwards, James P. |
| contents | We study low energy photons coupled to scalar and spinor matter in the presence of an arbitrary homogeneous electromagnetic field in a first-quantised (worldline) approach. Utilising 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 linearisation operator.
To treat the linearisation, several techniques are employed, including a functional expansion based on the proper time formalism and worldline Green functions, linearised 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 function for this path integral satisfying homogeneous Dirichlet boundary conditions and momentum space vertex operators representing the scattering photons already in momentum space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22308 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low-energy multi-photon scattering at tree-level and one-loop order in a homogeneous electromagnetic field Ahumada, Ivan Copinger, Patrick Edwards, James P. High Energy Physics - Theory High Energy Physics - Phenomenology We study low energy photons coupled to scalar and spinor matter in the presence of an arbitrary homogeneous electromagnetic field in a first-quantised (worldline) approach. Utilising 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 linearisation operator. To treat the linearisation, several techniques are employed, including a functional expansion based on the proper time formalism and worldline Green functions, linearised 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 function for this path integral satisfying homogeneous Dirichlet boundary conditions and momentum space vertex operators representing the scattering photons already in momentum space. |
| title | Low-energy multi-photon scattering at tree-level and one-loop order in a homogeneous electromagnetic field |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2507.22308 |