A note on the asymptotic symmetries of electromagnetism
Oscar Fuentealba, Marc Henneaux, Cédric Troessaert
Abstract
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 $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> (1) transformations (abelian algebra with invertible central term) while those of the $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> ( r ) transformations are conjugate to those of the subleading $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> ( 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.