The aliasing problem in lattice field theory
  The intrinsically nonlinear nature of quantum field theory provides a fundamental complication for lattice calculations, when the physical implications of the subtleties of Fourier theory are taken into account. Even though the fundamental fields are constrained to the first Brillouin zone, Fourier theory tells us that the high-momentum components of products of these fields "bleed into" neighbouring Brillouin zones, where they "alias" (or "masquerade") as low-momentum contributions, violating the conservation of energy and momentum, and fundamentally distorting calculations. In this paper I offer a general strategy for eliminating the artefacts of aliasing in practical calculations. 
John P. Costella