Scaling Limits of Lattice Quantum Fields by Wavelets

Morinelli V, Morsella G, Stottmeister A, Tanimoto Y (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

DOI: 10.1007/s00220-021-04152-5

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.

Involved external institutions

Università degli Studi di Roma 'Tor Vergata' IT Italy (IT) Gottfried Wilhelm Leibniz Universität Hannover DE Germany (DE)

How to cite

APA:

Morinelli, V., Morsella, G., Stottmeister, A., & Tanimoto, Y. (2021). Scaling Limits of Lattice Quantum Fields by Wavelets. Communications in Mathematical Physics. https://dx.doi.org/10.1007/s00220-021-04152-5

MLA:

Morinelli, Vincenzo, et al. "Scaling Limits of Lattice Quantum Fields by Wavelets." Communications in Mathematical Physics (2021).

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