A note on the asymptotic symmetries of electromagnetism

Abstract

We extend the asymptotic symmetries of electromagnetism in order to consistently include angle-dependent $u(1)$ gauge transformations $\epsilon$ that involve terms growing at spatial infinity linearly and logarithmically in $r$, $\epsilon \sim a(\theta ,\phi )r+b(\theta ,\phi )\ln r+c(\theta ,\phi )$. The charges of the logarithmic $u(1)$ transformations are found to be conjugate to those of the $\mathcal{O}(1)$ transformations (abelian algebra with invertible central term) while those of the $\mathcal{O}(r)$ transformations are conjugate to those of the subleading $\mathcal{O}(r^{-1})$ transformations. Because of this structure, one can decouple the angle-dependent $u(1)$ asymptotic symmetry from the Poincaré algebra, just as in the case of gravity: the generators of these internal transformations are Lorentz scalars in the redefined algebra. This implies in particular that one can give a definition of the angular momentum which is free from $u(1)$ gauge ambiguities. The change of generators that brings the asymptotic symmetry algebra to a direct sum form involves non linear redefinitions of the charges. Our analysis is Hamiltonian throughout and carried at spatial infinity.

25 pages, no figures. One note added and minor typos corrected. Matches with published version

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