The exponential decay of lattice Green functions is one of the main technical ingredients of the Balaban'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.
Dybalski, W., Stottmeister, A., Tanimoto, Y. (2024). Lattice Green functions for pedestrians: Exponential decay. REVIEWS IN MATHEMATICAL PHYSICS [10.1142/S0129055X2430005X].
Lattice Green functions for pedestrians: Exponential decay
Alexander Stottmeister;Yoh Tanimoto
2024-01-01
Abstract
The exponential decay of lattice Green functions is one of the main technical ingredients of the Balaban'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.File in questo prodotto:
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