Classical general relativity as BF-Plebanski theory with linear constraints
Classical general relativity as BF-Plebanski theory with linear constraints
复制标题
经典广义相对论为具有线性约束的 BF-Plebanski 理论
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
D. Oriti
中科院分区：
文献类型：
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作者：
Steffen Gielen;D. Oriti
我们本着 Plebanski 公式的精神，根据约束 BF 理论研究了连续 4D 引力的公式，但仅涉及线性约束，这种类型最近在量子引力的自旋泡沫方法中使用。我们确定了量子离散环境中使用的线性简单约束的连续版本和二次体积约束的线性版本，它们是完成从拓扑理论到引力的还原所必需的。我们还说明并讨论了相同连续线性约束的离散对应部分。此外，我们还展示了在哪些附加条件下离散体积约束遵循简单性约束，从而发挥次要约束的作用。
We investigate a formulation of continuum 4D gravity in terms of a constrained BF theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. We identify both the continuum version of the linear simplicity constraints used in the quantum discrete context and a linear version of the quadratic volume constraints that are necessary to complete the reduction from the topological theory to gravity. We also illustrate and discuss the discrete counterpart of the same continuum linear constraints. Moreover, we show under which additional conditions the discrete volume constraints follow from the simplicity constraints, thus playing the role of secondary constraints.