2005/02/28 by Kirill Krasnov, Jorma Louko
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Computer science #Cosmology and Gravitation Theories #Feynman diagram #Feynman integral #Geometry #Lorentz transformation #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Product (mathematics) #Propagator #Pure mathematics #Quantum mechanics #Representation (politics) #Space (punctuation) #Type (biology) #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1063/1.2180626
published as J.Math.Phys. 47 (2006) 033513 · 20 pages, 1 figure. v2: Case d=1 corrected, case d>1 clarified
arxiv created 2006/02/02 · openalex publication_date 2006/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We use AdS/CFT inspired methods to study the Racah coefficients for type I representations of the Lorentz group SO0(1,d+1) with d>1. For such representations (a multiple of) the Racah coefficient can be represented as an integral of a product of six bulk-to-bulk propagators over four copies of the hyperbolic space Hd+1. To compute the integrals we represent the bulk-to-bulk propagators in terms of bulk-to-boundary ones. The bulk integrals can be computed explicitly, and the boundary integrations are carried out by introducing Feynman parameters. The final result is an integral representation of the Racah coefficient given by four Barnes-Mellin type integrals.