1998/07/31 by Stefan Davids
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Extension (predicate logic) #Geometry #Lie group #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum mechanics #Semiclassical physics #Series (stratigraphy) #Simple (philosophy) #Tetrahedron #Unitary representation #Unitary state #gr-qc
paper · pdf · doi:10.1063/1.533171
published as J.Math.Phys.41:924-943,2000 · Latex2e - 26 pages, 6 figures. Uses AMS-fonts, AMS-LaTeX, epsf.tex and texdraw. Revised version with improved clarity and additional results
arxiv created 1998/11/24 · openalex publication_date 2000/02/01 · arxiv updated 2011/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We explore the geometry and asymptotics of extended Racah coefficients. The extension is shown to have a simple relationship to the Racah coefficients for the positive discrete unitary representation series of SU(1,1) which is explicitly defined. Moreover, it is found that this extension may be geometrically identified with two types of Lorentzian tetrahedra for which all the faces are timelike. The asymptotic formulas derived for the extension are found to have a similar form to the standard Ponzano–Regge asymptotic formulas for the SU(2) 6j symbol and so should be viable for use in a state sum for three dimensional Lorentzian quantum gravity.