Speaker
Description
I will discuss formally exact Hamiltonian representations of quantum field theories based on Daubechies wavelets. Daubechies wavelets are an orthonormal basis of compactly supported functions on the real line. They are generated from the fixed point of a renormalization group equation by translations and dyadic scale transformations.
There are an infinite number of basis functions with support in any open set. Using this basis local fields can be expressed as infinite linear combinations well-defined local observables. In this representation ill-defined local products of fields are replaced by infinite linear combinations of products of well-defined operators.
This can be applied to express all ten Poincaré generators as infinite linear combinations of products of well defined operators. The wavelet representation of the theory has natural volume and resolution cutoffs, and the dynamical operators at different resolution are self-similar, where the coefficients of operators different scales can be computed exactly using renormalization group methods. The method can be applied to both canonical or light front formulations of quantum field theory. I will discuss their potential use in real-time path integrals and some speculations on how to apply multi-scale methods to construct irreducible algebras of locally gauge invariant observables for use in gauge theories.
