Abstract
We study 6j-symbols or Racah coefficients for the tensor products of infinite-dimensional unitary principal series representations of the group SL(2, 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.
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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 198, No. 1, pp. 32–53, January, 2019.
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Derkachov, S.E., Spiridonov, V.P. The 6j-Symbols for the SL(2, ℂ) Group. Theor Math Phys 198, 29–47 (2019). https://doi.org/10.1134/S0040577919010033
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DOI: https://doi.org/10.1134/S0040577919010033