How do you renormalize the Schrodinger picture wave functional?

Question

So we know that correlation functions computed in a quantum field theory generically have to be renormalized, e.g. by introducing counterterms into the action, which remove UV divergences and leave the physical correlation functions dependent on renormalized couplings.  Now in the Schrodinger picture, we can compute correlation functions (at equal time) as moments of the evolving wave functional.  Presumably renormalization of the couplings in the Lagrangian through counterterms leads to additional pieces in the wave functional which ensure that its equal-time correlators are the appropriate renormalized ones.  I am wondering what the procedure is to account for this in evolving the wave functional, or if there is a particularly helpful paper, lecture, etc.

Comments

The action defines implicitly the representation of the Poincare group, and hence the way the wave functional propagates. The wave functional is quite arbitray, as it is the analogue of a wave function in QM; the dynamics is in the Hamiltonian, the generator of the time translations. This gets renormalized through the usual procedure,

I don't think that there is anything special to UV renormalization in the wave functional representation, the differences to the usual Fock space treatment show mostly in the IR, where the Fock approach is not flexible enough and misses, e,g, solitonic contributions.