Coherent states and 6j symbols' asymptotics

来源 :The XXIX International Colloquium on Group-Theoretical Metho | 被引量 : 0次 | 上传用户:michaelbing
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  Coherent states proved to be useful both in defining spin foam models of Quantum Gravity as well as in deriving their asymptotic limits.The method of coherent states combined with stationary point analysis gives nice geometric interpretation of contributions to asymptotic expansion and dominating phase of each term.It is,however,very inefficient in providing full expansion due to problems with computation of the Hessian determinant.Even in the case of 6j symbols where Ponzano-Regge formula is well known,it was not obtained this way so far.By the slight modification of the method we circumvented the problem.We are able to prove conjectured alternating cos/sin form of the full asymptotic expansion,as well as derive different form of the next to leading order term.The latest can be obtained by a symmetric recursion relation similar to proposed by Bonzom-Livine but applicable to 6j symbol itself not its square.Our method works both in 3D euclidean and lorentzian case.
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