In this work, we perform the Hamilton–Jacobi analysis of a modified gravity action, the so-called Freidel–Starodubtsev model. The complete set of involutive Hamiltonians that guarantee the system’s integrability is obtained. The generalized Poisson brackets are calculated in the metric phase by means of a suitable constraint matrix inversion. We also present a discussion about the metric and non-metric degrees of freedom. From the fundamental differential we recover the equations of motion and explicitly obtain the generators of local Lorentz transformations and also diffeomorphisms for the tetrad and the spin connection fields.

中文翻译：

---

弗赖德尔-斯塔达杜布采夫高炉（A）dS重力作用的汉密尔顿-雅各比分析

在这项工作中，我们对修正的重力作用（所谓的Freidel–Starodubtsev模型）进行了Hamilton–Jacobi分析。获得了确保系统可集成性的完整的对合哈密顿量。广义泊松括号是通过适当的约束矩阵求逆在度量阶段计算的。我们还提出了关于度量自由度和非度量自由度的讨论。从基本微分中，我们恢复了运动方程，并明确获得了局部Lorentz变换的生成器以及四面体和自旋连接场的亚纯。