TY - JOUR

T1 - Lattice Green functions for pedestrians

T2 - Exponential decay

AU - Dybalski, Wojciech

AU - Stottmeister, Alexander

AU - Tanimoto, Yoh

N1 - Publisher Copyright: © 2024 by the Authors.

PY - 2024/3/12

Y1 - 2024/3/12

N2 - The exponential decay of lattice Green functions is one of the main technical ingredients of the Ba{\l}aban's approach to renormalization. We give here a self-contained proof, whose various ingredients were scattered in the literature. The main sources of exponential decay are the Combes-Thomas method and the analyticity of the Fourier transforms. They are combined using a renormalization group equation and the method of images.

AB - The exponential decay of lattice Green functions is one of the main technical ingredients of the Ba{\l}aban's approach to renormalization. We give here a self-contained proof, whose various ingredients were scattered in the literature. The main sources of exponential decay are the Combes-Thomas method and the analyticity of the Fourier transforms. They are combined using a renormalization group equation and the method of images.

KW - math-ph

KW - math.MP

KW - renormalization

KW - propagators

KW - Quantum field theory

UR - http://www.scopus.com/inward/record.url?scp=85187924170&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2303.10754

DO - 10.48550/arXiv.2303.10754

M3 - Article

VL - 36

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

IS - 6

M1 - 2430005

ER -