  We study the effect of interactions on the time reversal invariant
topological insulators in four and three spatial dimensions. Their topological
indices are expressed by the interacting Green's functions. Under the local
self-energy approximation, we find that interaction could induce nontrivial
frequency-domain winding numbers and change the topological classes of the
system. Our results suggest that the topological phases could be destroyed
without developing long range orders. Practical issues on the accurate
frequency-momentum integration combined with DMFT and diagrammatic calculations
of the interacting Green's functions are also addressed.
