Geodesic
Racah coefficients for the group $\mathrm{SL}(2,\mathbb{R})$
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 28, Tome 509 (2021), pp. 99-112

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is devoted to the derivation of a universal integral representation for $6j$-symbols, or Racah coefficients, for the tensor product of three unitary representations of the main series of the group $\mathrm{SL}(2,\mathbb{R})$. The problem of calculating $6j$-symbols admits a natural reformulation in the language of Feynman diagrams. The original diagram can be significantly simplified and reduced to a basic diagram using the Gorishnii–Isaev method. In the case of representations of the main series, a closed expression in the form of the Mellin–Barnes integral is obtained for the basic diagram. 
@article{ZNSL_2021_509_a6,
     author = {S. E. Derkachev and A. V. Ivanov},
     title = {Racah coefficients for the group $\mathrm{SL}(2,\mathbb{R})$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {99--112},
     publisher = {mathdoc},
     volume = {509},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a6/}
}
TY  - JOUR
AU  - S. E. Derkachev
AU  - A. V. Ivanov
TI  - Racah coefficients for the group $\mathrm{SL}(2,\mathbb{R})$
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2021
SP  - 99
EP  - 112
VL  - 509
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a6/
LA  - ru
ID  - ZNSL_2021_509_a6
ER  - 
%0 Journal Article
%A S. E. Derkachev
%A A. V. Ivanov
%T Racah coefficients for the group $\mathrm{SL}(2,\mathbb{R})$
%J Zapiski Nauchnykh Seminarov POMI
%D 2021
%P 99-112
%V 509
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a6/
%G ru
%F ZNSL_2021_509_a6
S. E. Derkachev; A. V. Ivanov. Racah coefficients for the group $\mathrm{SL}(2,\mathbb{R})$. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 28, Tome 509 (2021), pp. 99-112. http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a6/