Group Analysis of Differential Equations and Integrable Systems − 2018


Vyacheslav Spiridonov (Joint Institute for Nuclear Research, Dubna & National Research University Higher School of Economics, Moscow, Russia)

$6j$-symbols for $SL(2,\mathbb{C})$ and Feynman diagrams

Abstract:
$6j$-symbols (Racah coefficients) for tensor products of unitary principal series representations of the $SL(2,\mathbb{C})$ group are computed using the Feynman diagrams technique. They are given either as a triple integral over the complex plane, or as an infinite bilateral sum of of the Mellin-Barnes type integrals. The final results differ from those obtained earlier by Ismagilov by particular transitions to equivalent representations.

This is a joint work with S.E. Derkachov.