Operator-algebraic renormalization and wavelets
Mathematical Physics
2021-12-13 v2 math.MP
Operator Algebras
Quantum Physics
Abstract
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
Cite
@article{arxiv.2002.01442,
title = {Operator-algebraic renormalization and wavelets},
author = {Alexander Stottmeister and Vincenzo Morinelli and Gerardo Morsella and Yoh Tanimoto},
journal= {arXiv preprint arXiv:2002.01442},
year = {2021}
}
Comments
6 pages, 3 figure (accepted version)