# Operator-algebraic renormalization and wavelets

February 04, 2020

We report on a rigorous operator-algebraic renormalization group scheme and
construct the continuum free field as the scaling limit of Hamiltonian lattice
systems using wavelet theory. A renormalization group step is determined by the
scaling equation identifying lattice observables with the continuum field
smeared by compactly supported wavelets. Causality follows from Lieb-Robinson
bounds for harmonic lattice systems. The scheme is related with the multi-scale
entanglement renormalization ansatz and augments the semi-continuum limit of
quantum systems.

Keywords:

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