Eur. Phys. J. C (2011) 71: 1646
https://doi.org/10.1140/epjc/s10052-011-1646-x

Regular Article - Theoretical Physics

Convergence of perturbation series for renormalization constants in Kraichnan model with “frozen” velocity field

¹ St. Petersburg State University, Physical Faculty, Ulyanovskaya Street, 3, 198504, Petrodvorets, St. Petersburg, Russia
² Institute for Analytical Instrumentation RAS, Rizhsky Prospect, 26, 198103, St. Petersburg, Russia

^* e-mail: Mikhail.Nalimov@pobox.spbu.ru

Received: 7 March 2011
Published online: 19 May 2011

Abstract

An instanton for the Kraichnan model with a ‘frozen’ velocity field is found. High-order asymptotics of the quantum-field perturbation expansion for the renormalization constant Z _ν are investigated. It is shown that this expansion is convergent, and the radius of convergence is calculated.