Renormalization of nonequilibrium dynamics at large N and finite temperature

We generalize a previously proposed renormalization and computation scheme for nonequilibrium dynamics to include finite temperature and one-loop self-consistency as arising in the large-N limit. Since such a scheme amounts essentially to tadpole resummation, it also includes, at high temperature, the hard mass corrections proportional to T². We present some numerical examples at $T=0$ and for finite temperature; the results reproduce the essential features of those of other groups. Especially we can confirm a recently discovered sum rule for the late time behavior.