Path integral representation of spin foam models of 4D gravity
Path integral representation of spin foam models of 4D gravity
复制标题
4D重力旋转泡沫模型的路径积分表示
DOI：
10.1088/0264-9381/25/24/245010
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发表时间：
2008
影响因子：
3.5
通讯作者：
L. Freidel
中科院分区：
文献类型：
--
作者：
Florian Conrady;L. Freidel
我们统一描述了最近由Engle， Livine， Pereira和Rovelli （ELPR）以及Freidel和Krasnov （FK）引入的所有自旋泡沫模型。我们证明了FK模型对于Immirzi参数γ的所有值都等价于离散理论的路径积分，并提供了相关作用的显式公式。讨论了FK模型和ELPR模型之间的关系，并研究了相应的边界状态。对于一般的Immirzi参数，这些由Alexandrov和Livine的SO(4)投影状态给出。对于0≤γ < 1，态可以被限制为SU(2)自旋网络。
We give a unified description of all recent spin foam models introduced by Engle, Livine, Pereira and Rovelli (ELPR) and by Freidel and Krasnov (FK). We show that the FK models are, for all values of the Immirzi parameter γ, equivalent to path integrals of a discrete theory and we provide an explicit formula for the associated actions. We discuss the relation between the FK and ELPR models and also study the corresponding boundary states. For general Immirzi parameter, these are given by Alexandrov's and Livine's SO(4) projected states. For 0 ⩽ γ < 1, the states can be restricted to SU(2) spin networks.