Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, 3j Symbols, and Character Localization |
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Authors: | Joseph Ben Geloun Razvan Gurau |
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Affiliation: | 1. Perimeter Institute for Theoretical Physics, 31, Caroline N., Waterloo, ON, N2L 2Y5, Canada 2. International Chair in Mathematical Physics and Applications (ICMPA?CUNESCO Chair), University of Abomey-Calavi, 072?B.P. 50, Cotonou, Republic of Benin
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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 DJMM¢(g){D^{J}_{MM'}(g)} . We use this result to derive asymptotic formulae for the character χ J (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 χ J (g) is in fact exact. The result hints at a “Duistermaat-Heckman like” localization property for discrete sums. |
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