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Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 198, Number 1, Pages 32–53
DOI: https://doi.org/10.4213/tmf9512 (Mi tmf9512) 		 
This article is cited in 16 scientific papers (total in 16 papers)

The $6j$-symbols for the $SL(2,\mathbb C)$ group

S. È. Derkacheva, V. P. Spiridonovb

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia
Full-text PDF (878 kB) Citations (16)
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DOI: https://doi.org/10.4213/tmf9512
Abstract: We study $6j$-symbols or Racah coefficients for the tensor products of infinite-dimensional unitary principal series representations of the group $SL(2,\mathbb C)$. Using the Feynman diagram technique, we reproduce the results of Ismagilov in constructing these symbols (up to a slight difference associated with equivalent representations). The resulting $6j$-symbols are expressed either as a triple integral over complex plane or as an infinite bilateral sum of integrals of the Mellin–Barnes type.
Keywords: $3j$-symbol, $6j$-symbol, Feynman diagram, $SL(2,\mathbb C)$ group, hypergeometric integral.
Funding agency Grant number
Russian Science Foundation 14-11-00598
This research is supported by a grant from the Russian Science Foundation (Project No. 14-11-00598).
Received: 20.11.2017
Revised: 20.11.2017
English version:
Theoretical and Mathematical Physics, 2019, Volume 198, Issue 1, Pages 29–47
DOI: https://doi.org/10.1134/S0040577919010033
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. È. Derkachev, V. P. Spiridonov, “The $6j$-symbols for the $SL(2,\mathbb C)$ group”, TMF, 198:1 (2019), 32–53; Theoret. and Math. Phys., 198:1 (2019), 29–47
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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