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Journal of Mathematical Sciences

, Volume 238, Issue 6, pp 819–833 | Cite as

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

  • P. A. ValinevichEmail author
  • S. E. Derkachov
  • A. P. Isaev
Article
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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.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • P. A. Valinevich
    • 1
    Email author
  • S. E. Derkachov
    • 1
  • A. P. Isaev
    • 2
  1. 1.St.Petersburg Department of Steklov Institute of MathematicsSt.PetersburgRussia
  2. 2.Bogoliubov Laboratory of Theoretical PhysicsJoint Institute of Nuclear ResearchDubnaRussia

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