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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 465, Pages 82–104 (Mi znsl6532)  
This article is cited in 1 scientific paper (total in 1 paper)

SOS-representation for the $SL(2,\mathbb C)$-invariant $R$-operator and Feynman diagrams

P. A. Valinevicha, S. E. Derkachova, A. P. Isaevb

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia
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Abstract: In the first part of the paper the basic facts about unitary seires representations of the group $SL(2,\mathbb C)$ and corresponding solutions to the Yang–Baxter equatins are given. In the second part we derive SOS-representation of the $R$-operator and prove the corresponding Yang–Baxter equation. Using Feynman diagrams we perform the calculation of the kernel of the R-operator in SOS-represetation. The expression for the kernel is presented in the form of Mellin–Barnes integral.
Key words and phrases: Yang–Baxter equation, $R$-matrix, $6j$-symbols.
Funding agency Grant number
Russian Science Foundation 14-11-00598
Received: 06.12.2017
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 238, Issue 6, Pages 819–833
DOI: https://doi.org/10.1007/s10958-019-04278-x
Document Type: Article
UDC: 517.9
Language: Russian
Citation: P. A. Valinevich, S. E. Derkachov, A. P. Isaev, “SOS-representation for the $SL(2,\mathbb C)$-invariant $R$-operator and Feynman diagrams”, Questions of quantum field theory and statistical physics. Part 24, Zap. Nauchn. Sem. POMI, 465, POMI, St. Petersburg, 2017, 82–104; J. Math. Sci. (N. Y.), 238:6 (2019), 819–833
Citation in format AMSBIB
\Bibitem{ValDerIsa17}
\by P.~A.~Valinevich, S.~E.~Derkachov, A.~P.~Isaev
\paper SOS-representation for the $SL(2,\mathbb C)$-invariant $R$-operator and Feynman diagrams
\inbook Questions of quantum field theory and statistical physics. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 465
\pages 82--104
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6532}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 238
\issue 6
\pages 819--833
\crossref{https://doi.org/10.1007/s10958-019-04278-x}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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