Geodesic
Group averaging for de~Sitter free fields in terms of hyperspherical functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 3, pp. 473-480

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We study the convergence of inner products of free fields over the homogeneous spaces of the de Sitter group and show that the convergence of inner products in the case of $N$-particle states is defined by the asymptotic behavior of hypergeometric functions. We calculate the inner product for two-particle states on the four-dimensional hyperboloid in detail.
Keywords: de Sitter group, group averaging, inner product, hyperspherical function, homogeneous space. 
@article{TMF_2010_164_3_a17,
     author = {V. V. Varlamov},
     title = {Group averaging for {de~Sitter} free fields in terms of hyperspherical functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {473--480},
     publisher = {mathdoc},
     volume = {164},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_164_3_a17/}
}
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V. V. Varlamov. Group averaging for de~Sitter free fields in terms of hyperspherical functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 3, pp. 473-480. http://geodesic.mathdoc.fr/item/TMF_2010_164_3_a17/