Determines the finite-energy one-loop soft-photon operator in QED, extracts a hard-hard residue in its commutator with Mellin-difference currents, and links it to a minimal filtered abelian extension and dipole-current Ward identities.
H¨ ormander,The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, vol
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Loop-level dipole currents and the renormalized hard celestial current algebra in QED
Determines the finite-energy one-loop soft-photon operator in QED, extracts a hard-hard residue in its commutator with Mellin-difference currents, and links it to a minimal filtered abelian extension and dipole-current Ward identities.