  We consider the scattering of massless particles coupled to an abelian gauge
field in 2n-dimensional Minkowski spacetime. Weinberg's soft photon theorem is
recast as Ward identities for infinitely many new nontrivial symmetries of the
massless QED S-matrix, with one such identity arising for each propagation
direction of the soft photon. These symmetries are identified as large gauge
transformations with angle-dependent gauge parameters that are constant along
the null generators of null infinity. Almost all of the symmetries are
spontaneously broken in the standard vacuum and the soft photons are the
corresponding Goldstone bosons. Our result establishes a relationship between
soft theorems and asymptotic symmetry groups in any even dimension.
