We study the Hamiltonian formalism of the non-minimally coupled Weyl connection gravity (NMCWCG) in order to check whether Ostrogradsky instabilities are present. The Hamiltonian of the NMCWCG theories is obtained by foliating space-time into a real line (representing time) and 3-dimensional space-like hypersurfaces, and by considering the spatial metric and the extrinsic curvature of the hypersurfaces as the canonical coordinates of the theory. Given the fact that the theory we study contains an additional dynamical vector field compared to the usual NMC models, which do not have Ostrogradsky instabilities, we are able to construct an effective theory without these instabilities, by constraining this Weyl field.

中文翻译：

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非最小耦合 Weyl 连接引力理论的 Ostrogradsky 不稳定性分析

我们研究了非最小耦合外尔连接引力 (NMCWCG) 的哈密顿形式主义，以检查是否存在 Ostrogradsky 不稳定性。NMCWCG 理论的哈密顿量是通过将时空叶理成一条实线（表示时间）和 3 维空间类超曲面，并将超曲面的空间度量和外在曲率视为理论的规范坐标来获得的. 鉴于与通常的 NMC 模型相比，我们研究的理论包含一个额外的动态矢量场，没有 Ostrogradsky 不稳定性，我们能够通过约束这个 Weyl 场来构建一个没有这些不稳定性的有效理论。