6j-Symbols for SL(2,C) Group and Feynman Diagrams

Explore the intricate world of Racah coefficients and 6j-symbols for tensor products of infinite-dimensional unitary principal series representations of the SL(2,C) group in this advanced mathematics lecture. Delve into the construction of these symbols using Feynman diagram techniques, contrasting with Ismagilov's earlier approach. Examine the resulting 6j-symbols, expressed as either a triple integral over complex plane or an infinite bilateral sum of Mellin-Barnes type integrals. This hour-long talk, part of the Hausdorff Trimester Program on Periods in Number Theory, Algebraic Geometry and Physics, presents joint work with S.E. Derkachov, offering a deep dive into complex mathematical concepts at the intersection of group theory and physics.