Lorentzian spin foam amplitudes: graphical calculus and asymptotics
Lorentzian spin foam amplitudes: graphical calculus and asymptotics
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DOI：
10.1088/0264-9381/27/16/165009
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发表时间：
2009-07
影响因子：
3.5
通讯作者：
J. Barrett;R. J. Dowdall;W. Fairbairn;F. Hellmann;R. Pereira
中科院分区：
文献类型：
--
作者：
J. Barrett;R. J. Dowdall;W. Fairbairn;F. Hellmann;R. Pereira
利用洛伦兹群的幺正表示的图形演算定义了量子引力自旋泡沫模型中4-单形的振幅。这种振幅的渐近性研究的限制时，表示参数是大的，对于各种情况下的边界数据。结果表明，对于边界数据对应于一个洛伦兹单纯形，渐近公式有两个条款，相位加上或减去洛伦兹签名雷吉行动的4-单纯形几何，乘以一个Immirzi参数。其他情况下的边界数据也被认为是，包括一个令人惊讶的贡献，从欧几里德签名度量。
The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graphical calculus for the unitary representations of the Lorentz group. The asymptotics of this amplitude are studied in the limit when the representation parameters are large, for various cases of boundary data. It is shown that for boundary data corresponding to a Lorentzian simplex, the asymptotic formula has two terms, with phase plus or minus the Lorentzian signature Regge action for the 4-simplex geometry, multiplied by an Immirzi parameter. Other cases of boundary data are also considered, including a surprising contribution from Euclidean signature metrics.