SOS-Representation for the SL(2,ℂ)-Invariant R-Operator and Feynman Diagrams

We discuss the construction of the SL(2, ℂ)-invariant R-operator acting in the tensor product of two principal series representations of SL(2, ℂ) and satisfying the Yang–Baxter equation. We present a closed-form expression for this R-operator as a multiple two-dimensional propagator-type Feynman integral, which can be reduced to a double integral of Mellin–Barnes type. The obtained R-operator can be interpreted as a Boltzmann weight of the corresponding SOS model. All necessary formulas concerning principal series representations of SL(2, ℂ) are presented.