The Bałaban variational problem in the non-linear sigma model

authored by: 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.
Organisation(s): Institute of Theoretical Physics
External Organisation(s): Adam Mickiewicz University, Poznań
Tor Vergata University of Rome
Type: Article
Journal: Reviews in mathematical physics
No. of pages: 53
ISSN: 0129-055X
Publication date: 30.10.2024
Publication status: E-pub ahead of print
Peer reviewed: Yes
ASJC Scopus subject areas: Statistical and Nonlinear Physics, Mathematical Physics
Electronic version(s): https://doi.org/10.48550/arXiv.2403.09800 (Access: Open)
https://doi.org/10.1142/S0129055X24610038 (Access: Closed)