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arXiv 0710.5017gr-qc
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新的自旋泡沫模型中的相干态、约束类和面积算符

Coherent states, constraint classes, and area operators in the new spin-foam models

Jonathan Engle, Roberto Pereira

备注：
21 pages; statements about gamma limits made more precise, and minor phrasing changes
发表信息：
Class.Quant.Grav.25:105010,2008
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摘要：

最近，在文献中出现了两个新的自旋泡沫模型，都是出于修改Barrett-Crane模型的愿望，以这种方式，施加某些第二类约束，称为交叉简单性约束，被削弱。我们将这两个模型称为FKLS模型和翻转模型。这两个模型都是基于交叉简单性约束的重新表述。本文主要分为两个部分。首先，我们澄清了重新制定的交叉简单性约束的结构和它们在新模型中的量子强加的性质。特别是，我们表明，在FKLS模型，量子交叉简单性意味着没有限制的状态。更深层次的原因是，由于FKLS的辛结构，在某种相关意义上，重新表述的交叉简单性约束现在是\emph{first class}，这导致施加约束的相干态方法，FKLS模型中的关键，不能给出任何状态限制。然而，交叉简单性仍然可以被看作是通过抑制动态传播中的缠绕自由度来实现的。在论文的第二部分，我们研究了模型中的面积谱。这两个研究的结果将突出显示，在翻转模型中，希尔伯特空间的状态，以及面积算符的频谱完全匹配的圈量子引力，而在FKLS（和Barrett-Crane）模型，边界希尔伯特空间和面积谱是不同的。

英文摘要：

Recently, two new spin-foam models have appeared in the literature, both motivated by a desire to modify the Barrett-Crane model in such a way that the imposition of certain second class constraints, called cross-simplicity constraints, are weakened. We refer to these two models as the FKLS model, and the flipped model. Both of these models are based on a reformulation of the cross-simplicity constraints. This paper has two main parts. First, we clarify the structure of the reformulated cross-simplicity constraints and the nature of their quantum imposition in the new models. In particular we show that in the FKLS model, quantum cross-simplicity implies no restriction on states. The deeper reason for this is that, with the symplectic structure relevant for FKLS, the reformulated cross-simplicity constraints, in a certain relevant sense, are now \emph{first class}, and this causes the coherent state method of imposing the constraints, key in the FKLS model, to fail to give any restriction on states. Nevertheless, the cross-simplicity can still be seen as implemented via suppression of intertwiner degrees of freedom in the dynamical propagation. In the second part of the paper, we investigate area spectra in the models. The results of these two investigations will highlight how, in the flipped model, the Hilbert space of states, as well as the spectra of area operators exactly match those of loop quantum gravity, whereas in the FKLS (and Barrett-Crane) models, the boundary Hilbert spaces and area spectra are different.

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