We perform, in a manifestly \(\mathrm{SO}(n-1,1)\) [\(\mathrm{SO}(n)\)] covariant fashion, the Hamiltonian analysis of general relativity in n dimensions written as a constrained BF theory. We solve the constraint on the B field in a way naturally adapted to the foliation of the spacetime that avoids explicitly the introduction of the vielbein. This leads to a form of the action involving a presymplectic structure, which is reduced by doing a suitable parametrization of the connection and then, after integrating out some auxiliary fields, the Hamiltonian form involving only first-class constraints is obtained.

中文翻译：

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n维高炉重力的直接哈密顿分析

我们执行，在一个明显\（\ mathrm {SO}（N-1,1）\） [ \（\ mathrm {SO}（N）\） ]协变方式，广义相对论在哈密顿分析Ñ写为尺寸受约束的BF理论。我们以自然适应时空变化的方式解决了对B场的约束，从而避免了明显引入vielbein。这导致涉及一种形式的先兆结构的动作，可以通过对连接进行适当的参数化来减小这种形式，然后在整合了一些辅助场之后，获得仅包含一等约束的哈密顿形式。