  We discuss the renormalisation of the initial value problem in quantum field
theory using the two-particle irreducible (2PI) effective action formalism. The
nonequilibrium dynamics is renormalised by counterterms determined in
equilibrium. We emphasize the importance of the appropriate choice of initial
conditions and go beyond the Gaussian initial density operator by defining
self-consistent initial conditions. We study the corresponding time evolution
and present a numerical example which supports the existence of a continuum
limit for this type of initial conditions.
