The Ponzano-Regge Asymptotic of the 6j Symbol: An Elementary Proof

Gurau R

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The Ponzano-Regge Asymptotic of the 6j Symbol: An Elementary Proof

机译：6j符号的Ponzano-Regge渐近线：基本证明

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In this paper we give a direct proof of the Ponzano-Regge asymptotic formula for the Wigner 6j symbol starting from Racah's single sum formula. Our method treats halfinteger and integer spins on the same footing. The generalization to Minkowskian tetrahedra is direct. All orders subleading contributions can be computed in this setting. This result should be relevant for the introduction of renormalization scales in spin foam models.

机译：本文从Racah的单和公式开始，直接证明了Wigner 6j符号的Ponzano-Regge渐近公式。我们的方法在相同的基础上处理半整数和整数旋转。 Minkowskian四面体的推广是直接的。可以在此设置中计算所有订单的主线索贡献。该结果与在旋转泡沫模型中引入重整化标度有关。

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《Annales Henri Poincare》 |2008年第7期|共12页
作者
Gurau R;
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正文语种 eng
中图分类高等数学;
关键词
GROUP FIELD-THEORY; RENORMALIZATION;

机译：群场理论;规范化;

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1. The Ponzano-Regge Asymptotic of the 6j Symbol: An Elementary Proof [J] . Gurau R Annales Henri Poincare . 2008,第7期

机译：6j符号的Ponzano-Regge渐近线：基本证明
2. Asymptotics of 6j and 10j symbols [J] . Freidel L., Louapre D. Classical and Quantum Gravity: An Interantional Journal of Gravity Geometry of Field Theories Supergravity Cosmology . 2003,第7期

机译：6j和10j符号的渐近性
3. Asymptotics of Wigner 3nj-symbols with small and large angular momenta: An elementary method [J] . Bonzom V., Fleury P. Journal of physics, A. Mathematical and theoretical . 2012,第7期

机译：具有大和小角动量的Wigner 3nj符号的渐近性：一种基本方法
4. The Screen Representation of Spin Networks: 2D Recurrence, Eigenvalue Equation for 6j Symbols, Geometric Interpretation and Hamiltonian Dynamics [C] . Roger W. Anderson, Vincenzo Aquilanti, Ana Carla Peixoto Bitencourt, International conference on computational science and its applications . 2013

机译：自旋网络的屏幕表示：二维递归，6j符号的特征值方程，几何解释和哈密顿动力学
5. Proof and proving in school mathematics instruction: Making the elementary grades part of the equation. [D] . Stylianides, Andreas J. 2005

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6. On a New Method in Elementary Number Theory Which Leads to An Elementary Proof of the Prime Number Theorem [O] . P. Erdös 1949

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7. The Ponzano-Regge asymptotic of the 6j symbol: an elementary proof [O] . Gurau, Razvan 2008

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8. Map Symbols and Lettering: A Two Part I.nvestigation. Part I An Examination of Map Symbols in Their Most Elementary Forms. Part II. The Logic of Automated Map Lettering [R] . Yoeli, P., Loon, J. 1972

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The Ponzano-Regge Asymptotic of the 6j Symbol: An Elementary Proof

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