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A bstract We extend the asymptotic symmetries of electromagnetism in order to consistently include angle-dependent u (1) gauge transformations ϵ that involve terms growing at spatial infinity linearly and logarithmically in r, ϵ ~ a (θ, φ) r + b (θ, φ) ln r + c (θ, φ). The charges of the logarithmic u (1) transformations are found to be conjugate to those of the O O (1) transformations (abelian algebra with invertible central term) while those of the O O (r) transformations are conjugate to those of the subleading O 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.
Fuentealba et al. (Mon,) studied this question.