Asymptotic Renormalization in Flat Space: Symplectic Potential and Charges of Electromagnetism

TL;DR

This paper develops a systematic method to renormalize the symplectic potential of electromagnetic fields at null infinity in higher-dimensional Minkowski space, leading to finite charges that reproduce QED soft theorems.

Contribution

It introduces a universal, local renormalization procedure for the symplectic potential in higher dimensions, connecting asymptotic charges with soft theorems in electromagnetism.

Findings

Renormalized charges reproduce QED soft theorems.

Counterterms make the symplectic potential finite at null infinity.

Method extends to higher dimensions and relates to holographic renormalization.

Abstract

We present a systematic procedure to renormalize the symplectic potential of the electromagnetic field at null infinity in Minkowski space. We work in $D\geq6$ spacetime dimensions as a toy model of General Relativity in $D\geq4$ dimensions. Total variation counterterms as well as corner counterterms are both subtracted from the symplectic potential to make it finite. These counterterms affect respectively the action functional and the Hamiltonian symmetry generators. The counterterms are local and universal. We analyze the asymptotic equations of motion and identify the free data associated with the renormalized canonical structure along a null characteristic. This allows the construction of the asymptotic renormalized charges whose Ward identity gives the QED soft theorem, supporting the physical viability of the renormalization procedure. We touch upon how to extend our analysis to the presence of logarithmic anomalies and upon how our procedure compares to holographic renormalization.