群场论和单纯引力路径积分：Holst-Plebanski引力模型
Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity
摘要：
在最近的工作中，作为非对易量子场论的群场论的对偶公式已经被提出，为约束BF理论提供了自旋泡沫模型和非对易单纯路径积分之间的精确对偶。在这个新的框架下，我们定义了一个模型的四维重力，其中包括Immirzi参数伽玛。它重现巴雷特起重机振幅时，伽玛到无穷大，但不同于现有的模型，否则，特别是它不需要任何合理性条件的伽玛。我们将振幅表示为具有显式非对易B变量的BF单纯路径积分和Wigner 15 j符号的自旋泡沫形式。最后，我们简要地讨论了相邻的单形之间的相关性，经常被认为是一个有问题的功能，例如，在巴雷特起重机模型。
英文摘要：
In a recent work, a dual formulation of group field theories as non-commutative quantum field theories has been proposed, providing an exact duality between spin foam models and non-commutative simplicial path integrals for constrained BF theories. In light of this new framework, we define a model for 4d gravity which includes the Immirzi parameter gamma. It reproduces the Barrett-Crane amplitudes when gamma goes to infinity, but differs from existing models otherwise; in particular it does not require any rationality condition for gamma. We formulate the amplitudes both as BF simplicial path integrals with explicit non-commutative B variables, and in spin foam form in terms of Wigner 15j-symbols. Finally, we briefly discuss the correlation between neighboring simplices, often argued to be a problematic feature, for example, in the Barrett-Crane model.
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