Operator-algebraic renormalization and wavelets

Alexander Stottmeister, Vincenzo Morinelli, Gerardo Morsella, Yoh Tanimoto
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.

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