标题： 从自旋泡沫到面积度规动力学到引力子 显示英文标题

标题： From spin foams to area metric dynamics to gravitons

摘要： 尽管自旋泡沫起源于长度度量自由度的量子化，但量子配置空间更基础的变量是面积。 这也由四维自旋泡沫模型的经典极限所突出，该极限由面积Regge作用量描述。 尽管面积Regge作用量对自旋泡沫至关重要，但其编码的动力学却了解甚少，特别是在连续极限中。 我们在此对由面积Regge作用量在规则中心细分的超立方格点上定义的动力学进行了系统研究。 选择这种格点可以避免非细分超立方格点的问题，因为在那些格点上面积Regge作用量是奇异的。 格点的规则性使得可以逐阶提取连续极限及其修正。 我们证明，与来自自旋泡沫平坦性问题的普遍预期相反，面积Regge作用量的连续极限在主导阶上描述了与广义相对论相同的引力子动力学。 长度度量有效作用量的下一阶修正项是格点常数的二阶项，它是一个在Weyl曲率张量中的二次项。 这一修正可以理解为源自面积度量的底层动力学。 这表明自旋泡沫动力学的连续极限确实导致无质量的引力子，并且主导阶的量子修正可以理解为从长度度量到面积度量配置空间的推广。 显示英文摘要

摘要： Although spin foams arose as quantizations of the length metric degrees of freedom, the quantum configuration space is rather based on areas as more fundamental variables. This is also highlighted by the semi-classical limit of four-dimensional spin foam models, which is described by the Area Regge action. Despite its central importance to spin foams the dynamics encoded by the Area Regge action is only poorly understood, in particular in the continuum limit. We perform here a systematic investigation of the dynamics defined by the Area Regge action on a regular centrally subdivided hypercubical lattice. This choice of lattice avoids many problems of the non-subdivided hypercubical lattice, for which the Area Regge action is singular. The regularity of the lattice allows to extract the continuum limit and its corrections, order by order in the lattice constant. We show that, contrary to widespread expectations which arose from the so-called flatness problem of spin foams, the continuum limit of the Area Regge action does describe to leading order the same graviton dynamics as general relativity. The next-to-leading order correction to the effective action for the length metric is of second order in the lattice constant, and is given by a quadratic term in the Weyl curvature tensor. This correction can be understood to originate from an underlying dynamics of area metrics. This suggests that the continuum limit of spin foam dynamics does lead to massless gravitons, and that the leading order quantum corrections can be understood to emerge from a generalization of the configuration space from length to area metrics.