  We investigate the asymptotic symmetry group of a scalar field
minimally-coupled to an abelian gauge field using the Hamiltonian formulation.
This extends previous work by Henneaux and Troessaert on the pure
electromagnetic case. We deal with minimally coupled massive and massless
scalar fields and find that they behave differently insofar as the latter do
not allow for canonically implemented asymptotic boost symmetries. We also
consider the abelian Higgs model and show that its asymptotic canonical
symmetries reduce to the Poincar\'e group in an unproblematic fashion.
