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arXiv · 2505.13247

Topology and the Infrared Structure of Quantum Electrodynamics

J. Gamboa
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Abstract

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.

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J. Gamboa. 2025-07-01. Topology and the Infrared Structure of Quantum Electrodynamics. https://arxiv.org/abs/2505.13247

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