Scaling limits of lattice quantum fields by wavelets
Abstract
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.
Cite
@article{arxiv.2010.11121,
title = {Scaling limits of lattice quantum fields by wavelets},
author = {Vincenzo Morinelli and Gerardo Morsella and Alexander Stottmeister and Yoh Tanimoto},
journal= {arXiv preprint arXiv:2010.11121},
year = {2021}
}
Comments
66 pages, 4 figure (accepted version)