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

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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. Derkachev^a, V. P. Spiridonov^b

^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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Linking options:

https://www.mathnet.ru/eng/tmf9512

https://doi.org/10.4213/tmf9512

https://www.mathnet.ru/eng/tmf/v198/i1/p32

This publication is cited in the following 16 articles:

G.A. Sarkissian, V.P. Spiridonov, “Complex and rational hypergeometric functions on root systems”, Journal of Geometry and Physics, 203 (2024), 105274
D. V. Artamonov, “Classical $6j$-symbols of finite-dimensional representations of the algebra $\mathfrak{gl}_3$”, Theoret. and Math. Phys., 216:1 (2023), 909–923
S. E. Derkachov, A. P. Isaev, L. A. Shumilov, “Ladder and zig-zag Feynman diagrams, operator formalism and conformal triangles”, J. High Energ. Phys., 2023:6 (2023), 59
E. Lanina, A. Sleptsov, “Tug-the-hook symmetry for quantum 6j-symbols”, Physics Letters B, 845 (2023), 138138
A. Bissi, S. Sarkar, “A constructive solution to the cosmological bootstrap”, J. High Energ. Phys., 2023:9 (2023), 115
Yu. A. Neretin, “On the Dotsenko–Fateev complex twin of the Selberg integral and its extensions”, Ramanujan J., 64 (2023), 37–55
S. E. Derkachev, A. V. Ivanov, “Racah Coefficients for the Group SL(2,ℝ)”, J Math Sci, 275:3 (2023), 289
S. E. Derkachov, G. A. Sarkissian, V. P. Spiridonov, “Elliptic hypergeometric function and $6j$-symbols for the $SL(2,\pmb{\mathbb C})$ group”, Theoret. and Math. Phys., 213:1 (2022), 1406–1422
S. E. Derkachev, A. V. Ivanov, L. A. Shumilov, “Mellin–Barnes Transformation for Two-Loop Master-Diagram”, J Math Sci, 264:3 (2022), 298
Neretin Yu.A., “An Analog of the Dougall Formula and of the de Branges-Wilson Integral”, Ramanujan J., 54:1 (2021), 93–106
S. E. Derkachev, A. V. Ivanov, “Koeffitsienty Raka dlya gruppy $\mathrm{SL}(2,\mathbb{R})$”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 28, Zap. nauchn. sem. POMI, 509, POMI, SPb., 2021, 99–112
V. F. Molchanov, Yu. A. Neretin, “A pair of commuting hypergeometric operators on the complex plane and bispectrality”, J. Spectr. Theory, 11:2 (2021), 509–586
Yury A. Neretin, “Barnes–Ismagilov Integrals and Hypergeometric Functions of the Complex Field”, SIGMA, 16 (2020), 072, 20 pp.
Gor A. Sarkissian, Vyacheslav P. Spiridonov, “The Endless Beta Integrals”, SIGMA, 16 (2020), 074, 21 pp.
S. E. Derkachev, A. V. Ivanov, L. A. Shumilov, “Preobrazovanie Mellina–Barnsa dlya dvukhpetlevoi master-diagrammy”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 27, Zap. nauchn. sem. POMI, 494, POMI, SPb., 2020, 144–167
Liu J., Perlmutter E., Rosenhaus V., Simmons-Duffin D., “D-Dimensional Syk, Ads Loops, and 6J Symbols”, J. High Energy Phys., 2019, no. 3, 052

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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