We introduce a covariant formulation of Barbero–Immirzi connections, which are used in Loop Quantum Gravity to describe gravity. We show that Barbero–Immirzi connections can be uniquely defined out of a given spin connection for any $(n+1)$-dimensional lorentzian manifold which is spin. A remarkable result is that the presence of a real Barbero–Immirzi parameter is a feature unique to the 4-dimensional case.

中文翻译：

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Barbero–Immirzi连接以及如何建立它们

我们介绍了Barbero–Immirzi连接的协变公式，该公式在回路量子重力中用于描述重力。我们显示，可以从给定旋转连接中任意定义Barbero–Immirzi连接的唯一性$（ñ+\mathrm{1个}）$维旋转的洛伦兹流形。一个了不起的结果是，真实的Barbero–Immirzi参数的存在是4维情况的独特功能。