  Daubechies wavelets are used to make an exact multi-scale decomposition of
quantum fields. For reactions that involve a finite energy that take place in a
finite volume, the number of relevant quantum mechanical degrees of freedom is
finite. The wavelet decomposition has natural resolution and volume truncations
that can be used to isolate the relevant degrees of freedom. The application of
flow equation methods to construct effective theories that decouple coarse and
fine scale degrees of freedom is examined.
