Asymptotes in SU(2) recoupling theory

• Verfasst von: Ben Geloun, Joseph [VerfasserIn]
• Verfasst von: Gurǎu, Rǎzvan [VerfasserIn]
• Titel: Asymptotes in SU(2) recoupling theory
• Titelzusatz: Wigner matrices, 3j symbols, and character localization
• Verf.angabe: Joseph Ben Geloun and Razvan Gurau
• E-Jahr: 2011
• Jahr: January 19, 2011
• Umfang: 42 S.
• Fussnoten: Gesehen am 28.09.2022
• Titel Quelle: Enthalten in: Institut Henri PoincaréAnnales Henri Poincaré
• Ort Quelle: Cham (ZG) : Springer International Publishing AG, 2000
• Jahr Quelle: 2011
• Band/Heft Quelle: 12(2011), 1, Seite 77-118
• ISSN Quelle: 1424-0661
• DOI: doi:10.1007/s00023-010-0072-1
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Angular Momentum Vector
• Sach-SW: Asymptotic Formula
• Sach-SW: Saddle Point
• Sach-SW: Saddle Point Approximation
• Sach-SW: Saddle Point Equation
• K10plus-PPN: 1805304925

Abstract

In this paper, we employ a technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index J) of generic Wigner matrix elements $${D^{J}_{MM'}(g)}$$. We use this result to derive asymptotic formulae for the character χJ(g) of an SU(2) group element and for Wigner’s 3j symbol. Surprisingly, given that we perform five successive layers of approximations, the asymptotic formula we obtain for χJ(g) is in fact exact. The result hints at a “Duistermaat-Heckman like” localization property for discrete sums.