Infrared Divergence in QED and the Fluctuation of Electromagnetic Fields

Abstract

We revisit infrared divergences in QED using a Fock space formulation and relate them to electromagnetic field fluctuations. We contrast this with both Faddeev--Kulish dressing and Morikawa's stochastic separation: gauge invariance enforces Bloch--Nordieck/Kinoshita--Lee--Nauenberg cancellation via coherent soft phases, whereas stochastic coarse-graining breaks this coherence. Callen--Welton fluctuations (Fluctuation--Dissipation Theorem) are quantum-coherent and do not justify Langevin noise for gauge fields, even in de~Sitter (Maxwell equations remain conformally invariant in four dimensions).