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Abstract

We investigate the asymptotic structure of electromagnetism in Minkowski
space in even and odd spacetime dimensions $\geq 4$. We focus on $d>4$ since
the case $d=4$ has been studied previously at length. We first consider spatial
infinity where we provide explicit boundary conditions that admit the known
physical solutions and make the formalism well defined (finite symplectic
structure and charges). Contrary to the situation found in $d=4$ dimensions,
there is no need to impose parity conditions under the antipodal map on the
leading order of the fields when $d>4$. There is, however, the same need to
modify the standard bulk symplectic form by a boundary term at infinity
involving a surface degree of freedom. This step makes the Lorentz boosts act
canonically. Because of the absence of parity conditions, the theory is found
to be invariant under two independent algebras of angle-dependent $u(1)$
transformations ($d>4$). We then integrate the equations of motion in order to
find the behaviour of the fields near null infinity. We exhibit the radiative
and Coulomb branches, characterized by different decays and parities. The
analysis yields generalized matching conditions between the past of
$\mathscr{I}^+$ and the future of $\mathscr{I} ^-$.