The paper is devoted to the derivation of a universal integral representation for 6j-symbols, or Racah coefficients, for the tensor product of three unitary representations of the principle series of the group SL(2, ℝ). The problem of calculating 6j-symbols admits a natural reformulation in the language of Feynman diagrams. The original diagram can be significantly simplified and reduced to a basic diagram using the Gorishnii–Isaev method. In the case of representations of the principle series, we obtained a closed expression in the form of the Mellin–Barnes integral for the basic diagram.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 509, 2021, pp. 99–112.
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Derkachev, S.E., Ivanov, A.V. Racah Coefficients for the Group SL(2,ℝ). J Math Sci 275, 289–298 (2023). https://doi.org/10.1007/s10958-023-06681-x
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DOI: https://doi.org/10.1007/s10958-023-06681-x