Scaling limits of lattice quantum fields by wavelets
Vincenzo Morinelli, Gerardo Morsella, Alexander Stottmeister, Yoh Tanimoto
October 21, 2020
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.
Keywords:algebraic quantum field theory, scaling limit, Quantum field theory on lattices, renormalization group methods, Wavelet theory