Geodesic
The~$6j$-symbols for the~$SL(2,\mathbb C)$ group
Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 1, pp. 32-53

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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.
Mots-clés : $3j$-symbol, $6j$-symbol
Keywords: Feynman diagram, $SL(2,\mathbb C)$ group, hypergeometric integral. 
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     author = {S. \`E. Derkachev and V. P. Spiridonov},
     title = {The~$6j$-symbols for the~$SL(2,\mathbb C)$ group},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     number = {1},
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S. È. Derkachev; V. P. Spiridonov. The~$6j$-symbols for the~$SL(2,\mathbb C)$ group. Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 1, pp. 32-53. http://geodesic.mathdoc.fr/item/TMF_2019_198_1_a2/