This article is cited in 12 papers

Nonlinear algebra and Bogoliubov's recursion

A. Yu. Morozov^a, M. N. Serbin<sup>abcde

a</sup> Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
^b N. N. Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine
^c L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
^d Moscow Institute of Physics and Technology
^e Museo Storico della Fisica e Centro Studi e Ricerche "Enrico Fermi"

Abstract: We give many examples of applying Bogoliubov's forest formula to iterative solutions of various nonlinear equations. The same formula describes an extremely wide class of objects, from an ordinary quadratic equation to renormalization in quantum field theory.

Keywords: quantum field theory, renormalization, nonlinear algebra.

Received: 02.04.2007

DOI: 10.4213/tmf6172

 English version: Theoretical and Mathematical Physics, 2008, 154:2, 270–293

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