Wavelet discretized field theory*

Local quantum fields can be expanded in a basis of Daubechies'
wavelets.  The basis functions are orthonormal, have compact support,
have some smoothness, and are constructed from the fixed point of a
renormalization group equation.  Wavelet expansions of fields have
natural volume and resolution cutoffs.  For truncations to finite
volume and resolution,  the equations of motion are well-defined on the
free-field Fock space.  The Hamiltonian of a local field theory in
this representation can be computed analytically, starting with a
small finite set of rational numbers, using renormalization group
methods.  The commutators in the dynamical equations can be computed
efficiently and analytically.  In this work it is demonstrated that
similarity renormalization group methods can be used to make effective
theories by eliminating short-distance degrees of freedom in a
truncated theory.  Unlike lattice methods, the resulting truncated fields have
some smoothness, there are systematic ways to add corrections, and the
corrections have identifiable scaling properties.  Some other
features of this representation are discussed.