Lorentzian spin foam amplitudes: graphical calculus and asymptotics

被引：152

作者：

Barrett, John W. ^{[1
]}

Dowdall, R. J. ^{[1
]}

Fairbairn, Winston J. ^{[1
]}

Hellmann, Frank ^{[1
]}

Pereira, Roberto ^{[2
]}

机构：

[1] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

[2] Ctr Phys Theor, F-13288 Marseille 9, France

来源：

CLASSICAL AND QUANTUM GRAVITY | 2010年 / 27卷 / 16期

基金：

英国工程与自然科学研究理事会;

关键词：

QUANTUM; FINITENESS; VARIABLES; NETWORKS; VERTEX;

D O I：

10.1088/0264-9381/27/16/165009

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

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.

引用

页数：34

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