# Scaling limits of lattice quantum fields by wavelets

October 21, 2020

We present a rigorous renormalization group scheme for lattice quantum field
theories in terms of operator algebras. The renormalization group is considered
as an inductive system of scaling maps between lattice field algebras. We
construct scaling maps for scalar lattice fields using Daubechies' wavelets,
and show that the inductive limit of free lattice ground states exists and the
limit state extends to the familiar massive continuum free field, with the
continuum action of spacetime translations. In particular, lattice fields are
identified with the continuum field smeared with Daubechies' scaling functions.
We compare our scaling maps with other renormalization schemes and their
features, such as the momentum shell method or block-spin transformations.

Keywords:

algebraic quantum field theory, scaling limit, Quantum field theory on lattices, renormalization group methods, Wavelet theory