Details
| Original language | English |
|---|---|
| Article number | 2461003 |
| Number of pages | 53 |
| Journal | Reviews in mathematical physics |
| Early online date | 30 Oct 2024 |
| Publication status | E-pub ahead of print - 30 Oct 2024 |
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.
Keywords
- Balaban's method, constructive QFT, Lattice field theory, nonlinear sigma models, Quantum field theory, variational calculus, Wilsonian renormalization
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
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In: Reviews in mathematical physics, 30.10.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The Bałaban variational problem in the non-linear sigma model
AU - Dybalski, Wojciech
AU - Stottmeister, Alexander
AU - Tanimoto, Yoh
N1 - Publisher Copyright: © 2024 The Author(s).
PY - 2024/10/30
Y1 - 2024/10/30
N2 - 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.
AB - 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.
KW - Balaban's method
KW - constructive QFT
KW - Lattice field theory
KW - nonlinear sigma models
KW - Quantum field theory
KW - variational calculus
KW - Wilsonian renormalization
UR - http://www.scopus.com/inward/record.url?scp=85208038306&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2403.09800
DO - 10.48550/arXiv.2403.09800
M3 - Article
AN - SCOPUS:85208038306
JO - Reviews in mathematical physics
JF - Reviews in mathematical physics
SN - 0129-055X
M1 - 2461003
ER -