The Bałaban variational problem in the non-linear sigma model

verfasst von

Wojciech Dybalski, Alexander Stottmeister, Yoh Tanimoto

Abstract

The minimization of the action of a QFT with a constraint dictated by the block averaging procedure is an important part of Bałaban's approach to renormalization. It is particularly interesting for QFTs with non-trivial target spaces, such as gauge theories or non-linear sigma models on a lattice. We analyze this step for the O(4) non-linear sigma model in two dimensions and demonstrate, in this case, how various ingredients of Bałaban's approach play together. First, using variational calculus on Lie groups, the equation for the critical point is derived. Then, this non-linear equation is solved by the Banach contraction mapping theorem. This step requires detailed control of lattice Green functions and their integral kernels via random walk expansions.

Organisationseinheit(en)

Institut für Theoretische Physik

Externe Organisation(en)

Adam-Mickiewicz-Universität Posen
Università degli studi di Roma Tor Vergata

Typ

Artikel

Journal

Reviews in mathematical physics

Anzahl der Seiten

53

ISSN

0129-055X

Publikationsdatum

30.10.2024

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Statistische und nichtlineare Physik, Mathematische Physik

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2403.09800 (Zugang: Offen)
https://doi.org/10.1142/S0129055X24610038 (Zugang: Geschlossen)