Abstract:

I discuss an exact discrete representation of local quantum field theory based on Daubechies wavelets.  The wavelet representation replaces ill-defined local products of operator valued distributions by infinite sums of products of well-defined operators.  The discrete degrees of freedom are localized and there is an irreducible algebra of canonical pairs of fields.  The representation has natural resolution and volume truncations.  The resolution truncated theories are self-similar and saisfy a functional renormalization group equation.  Non-pertrubative calculations can be performed by diagonailzing resolution and volume truncated Hamiltonians.  This reduces the dynamical problem to finite linear algebra.   The representation is natural for quantum computing since the truncated theory is discrete, canonical and almost local.

Invited talk for  ``Hamiltonian Field Theory for QCD and Hadron Physics",  Granada, Spain 5/23