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We study 6j-symbols, or Racah coefficients for tensor products ofinfinite-dimensional unitary principal series representations of the groupSL(2,C). These symbols were constructed earlier by Ismagilov and we rederivehis result (up to some slight difference associated with equivalentrepresentations) using the Feynman diagrams technique. The resulting 6j-symbolsare expressed either as a triple integral over complex plane with a symmetrickernel or as an infinite bilateral sum of integrals of the Mellin-Barnes type.

On the 6j-symbols for SL(2,C) group