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Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 200, Number 2, Pages 290–309
DOI: https://doi.org/10.4213/tmf9668 (Mi tmf9668) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Quasirenormalizable quantum field theories

M. V. Polyakovab, K. M. Semenov-Tian-Shanskybc, A. O. Smirnovd, A. A. Vladimirove

a Ruhr-Universität Bochum, Fakultät für Physik und Astronomie, Institut für Theoretische Physik II, Bochum, Germany
b Petersburg Nuclear Physics Institute, National Research Center Kurchatov Institute, Gatchina, Russia
c St. Petersburg National Research Academic University of the~Russian Academy of Sciences, St. Petersburg, Russia
d St. Petersburg State University of Aerospace Instrumentation, St. Petersburg, Russia
e Universität Regensburg, Institut für Theoretische Physik, Regensburg, Germany
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DOI: https://doi.org/10.4213/tmf9668
Abstract: Leading logarithms in massless nonrenormalizable effective field theories can be computed using nonlinear recurrence relations. These recurrence relations follow from the fundamental requirements of unitarity, analyticity, and crossing symmetry of scattering amplitudes and generalize the renormalization group technique to the case of nonrenormalizable effective field theories. We review the existing exact solutions of nonlinear recurrence relations relevant for field theory applications. We introduce a new class of quantum field theories (quasirenormalizable field theories) in which resumming leading logarithms for $2\to2$ scattering amplitudes yields a possibly infinite number of Landau poles.
Keywords: renormalization group, effective field theory, leading logarithm, Landau pole, Dixon elliptic function.
Funding agency Grant number
Deutsche Forschungsgemeinschaft CRC110
Russian Foundation for Basic Research 18-51-18007
The research of M. V. Polyakov and K. M. Semenov-Tian-Shansky was supported by the DFG (Grant No. CRC110). The research of A. O. Smirnov was supported by the Russian Foundation for Basic Research (Grant No. 18-51-18007).
Received: 03.12.2018
Revised: 19.01.2019
English version:
Theoretical and Mathematical Physics, 2019, Volume 200, Issue 2, Pages 1176–1192
DOI: https://doi.org/10.1134/S0040577919080105
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. V. Polyakov, K. M. Semenov-Tian-Shansky, A. O. Smirnov, A. A. Vladimirov, “Quasirenormalizable quantum field theories”, TMF, 200:2 (2019), 290–309; Theoret. and Math. Phys., 200:2 (2019), 1176–1192
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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