  We study the dynamics of interacting fermions in the continuum. Our approach
uses the concept of lattice-localized frames, which we introduce here. We first
prove a Lieb-Robinson bound that is valid for a general class of local
interactions, which implies the existence of the dynamics at the level of the
CAR algebra. We then turn to the physical situation relevant to the
(fractional) quantum Hall effect, namely the quasi-free second quantized Landau
Hamiltonian to which electron-electron interactions can be added.
