Topology and the Infrared Structure of Quantum Electrodynamics
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916820637712384 |
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| author | Gamboa, J. |
| author_facet | Gamboa, J. |
| contents | We study infrared divergences in quantum electrodynamics using geometric phases and the adiabatic approximation in quantum field theory. In this framework, the asymptotic \textit{in} and \textit{out} states are modified by Berry phases, $e^{i Δα_{\text{in}}}$ and $e^{i Δα_{\text{out}}}$, which encode the infrared structure non-perturbatively and regulate soft-photon divergences.
Unlike the Faddeev--Kulish formalism, which employs perturbative dressing with coherent states, our approach reformulates the effective action in terms of Berry connections in field space. This yields finite, gauge-invariant scattering amplitudes without requiring a sum over soft-photon emissions.
We show that infrared divergences cancel to all orders in the bremsstrahlung vertex function $Γ^μ(p_1, p_2)$, due to destructive interference among inequivalent Berry phases. As an application, we study the formation of positronium in the infrared regime and argue that the dressed \(S\)-matrix exhibits a functional singularity at $s = 4 m_e^2$, corresponding to a physical pole generated by topological flux. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topology and the Infrared Structure of Quantum Electrodynamics Gamboa, J. High Energy Physics - Theory High Energy Physics - Phenomenology We study infrared divergences in quantum electrodynamics using geometric phases and the adiabatic approximation in quantum field theory. In this framework, the asymptotic \textit{in} and \textit{out} states are modified by Berry phases, $e^{i Δα_{\text{in}}}$ and $e^{i Δα_{\text{out}}}$, which encode the infrared structure non-perturbatively and regulate soft-photon divergences. Unlike the Faddeev--Kulish formalism, which employs perturbative dressing with coherent states, our approach reformulates the effective action in terms of Berry connections in field space. This yields finite, gauge-invariant scattering amplitudes without requiring a sum over soft-photon emissions. We show that infrared divergences cancel to all orders in the bremsstrahlung vertex function $Γ^μ(p_1, p_2)$, due to destructive interference among inequivalent Berry phases. As an application, we study the formation of positronium in the infrared regime and argue that the dressed \(S\)-matrix exhibits a functional singularity at $s = 4 m_e^2$, corresponding to a physical pole generated by topological flux. |
| title | Topology and the Infrared Structure of Quantum Electrodynamics |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2505.13247 |