  A new splitting is proposed for solving the Vlasov-Maxwell system. This
splitting is based on a decomposition of the Hamiltonian of the Vlasov-Maxwell
system and allows for the construction of arbitrary high order methods by
composition (independent of the specific deterministic method used for the
discretization of the phase space). Moreover, we show that for a spectral
method in space this scheme satisfies Poisson's equation without explicitly
solving it. Finally, we present some examples in the context of the time
evolution of an electromagnetic plasma instability which emphasizes the
excellent behavior of the new splitting compared to methods from the
literature.
