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Functional Fourier transformation and renormalization group transformation in bosonic field theory models. (English. Russian original) Zbl 1280.81091

Theor. Math. Phys. 174, No. 2, 263-272 (2013); translation from Teor. Mat. Fiz. 174, No. 2, 303-312 (2013).
Summary: We introduce the notion of a functional Fourier transformation in bosonic \(p\)-adic and Euclidean models of statistical physics. We prove a commutation relation between the Fourier transformation and the Wilson renormalization group transformation and discuss the similarity of renormalization group formalisms in \(p\)-adic and Euclidean models.

MSC:

81T10 Model quantum field theories
81T17 Renormalization group methods applied to problems in quantum field theory
82B28 Renormalization group methods in equilibrium statistical mechanics
11E95 \(p\)-adic theory
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
82B10 Quantum equilibrium statistical mechanics (general)
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