Email this article The 6j-Symbols for the SL(2, ℂ) Group
- Authors: Derkachov S.E.1, Spiridonov V.P.2
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Affiliations:
- St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
- Bogoliubov Laboratory of Theoretical Physics
- Issue: Vol 198, No 1 (2019)
- Pages: 29-47
- Section: Article
- URL: https://journals.rcsi.science/0040-5779/article/view/172072
- DOI: https://doi.org/10.1134/S0040577919010033
- ID: 172072
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Abstract
We study 6j-symbols or Racah coefficients for the tensor products of infinite-dimensional unitary principal series representations of the group SL(2, ℂ). Using the Feynman diagram technique, we reproduce the results of Ismagilov in constructing these symbols (up to a slight difference associated with equivalent representations). The resulting 6j-symbols are expressed either as a triple integral over complex plane or as an infinite bilateral sum of integrals of the Mellin–Barnes type.
About the authors
S. E. Derkachov
St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Author for correspondence.
Email: derkach@pdmi.ras.ru
Russian Federation, St. Petersburg
V. P. Spiridonov
Bogoliubov Laboratory of Theoretical Physics
Author for correspondence.
Email: spiridon@theor.jinr.ru
Russian Federation, Dubna, Moscow Oblast
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