The 6j-Symbols for the SL(2, ℂ) Group

Resumo

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.