Theoretical and Mathematical Physics

, Volume 198, Issue 1, pp 29–47 | Cite as

The 6j-Symbols for the SL(2, ℂ) Group

  • S. E. DerkachovEmail author
  • V. P. SpiridonovEmail author


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.


3j-symbol 6j-symbol Feynman diagram SL(2,ℂ) group hypergeometric integral 


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of SciencesSt. PetersburgRussia
  2. 2.Bogoliubov Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubnaRussia

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