TY - JOUR

T1 - Scaling Limits of Lattice Quantum Fields by Wavelets

AU - Morinelli, Vincenzo

AU - Morsella, Gerardo

AU - Stottmeister, Alexander

AU - Tanimoto, Yoh

N1 - Funding Information: AS would like to thank Tobias J. Osborne and Reinhard F. Werner for useful discussions and comments. VM thanks Domenico Marinucci and Claudio Durastanti for comments and discussions. AS was in part supported by Alexander-von-Humboldt Foundation through a Feodor Lynen Return Fellowship. The European Research Council Advanced Grant 669240 QUEST supported VM and partially GM. VM was supported by Indam from March 2019 to February 2020. Until February 2020 YT was supported by Programma per giovani ricercatori, anno 2014 “Rita Levi Montalcini” of the Italian Ministry of Education, University and Research. VM, GM and YT also acknowledge the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome “Tor Vergata”, CUP E83C18000100006 and the University of Rome “Tor Vergata” funding scheme “Beyond Borders”, CUP E84I19002200005. Open Access funding enabled and organized by Projekt DEAL.

PY - 2021/10

Y1 - 2021/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85112026472&partnerID=8YFLogxK

U2 - 10.1007/s00220-021-04152-5

DO - 10.1007/s00220-021-04152-5

M3 - Article

VL - 387

SP - 299

EP - 360

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -