Functional Fourier transformation and renormalization group transformation in bosonic field theory models

M. D. Missarov

Kazan (Privolzhskii) Federal University, Kazan, Russia

Abstract: 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.

Keywords: bosonic model, renormalization group, Fourier transformation, hierarchical lattice, $p$-adic model, Euclidean model.

Received: 27.09.2012

DOI: 10.4213/tmf8415

 English version: Theoretical and Mathematical Physics, 2013, 174:2, 263–272

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