We constructed a symplectic realization of the dynamic structure of two interacting spin-two fields in three dimensions. A significant simplification refers to the treatment of constraints: instead of performing a Hamiltonian analysis à la Dirac, we worked out a method that only uses properties of the pre-symplectic two-form matrix and its corresponding zero-modes to investigate the nature of constraints and the gauge structure of the theory. For instance, we demonstrate that the contraction of the zero-modes with the potential gradient, yields explicit expressions for the whole set of constraints on the dynamics of the theory, including the symmetrization condition and an explicit relationship between the coupling and cosmological constants. This way, we further identify the necessary conditions for the existence of a unique non-linear candidate for a partially massless theory, using only the expression for the interaction parameters of the model. In the case of gauge structure, the transformation laws for the entire set of dynamical variables are more straightforwardly derived from the structure of the remaining zero-modes; in this sense, the zero-modes must be viewed as the generators of the corresponding gauge transformations. Thereafter, we use an appropriate gauge-fixing procedure, the time gauge, to compute both the quantization brackets and the functional measure on the path integral associated with our model. Finally, we confirm that three-dimensional bi-gravity has two physical degrees of freedom per space point. With the above, we provide a new perspective for a better understanding of the dynamical structure of theories of interacting spin-two fields, which does not require the constraints to be catalogued as first- and second-class ones as in the case of Dirac’s standard method.

中文翻译：

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两个相互作用的自旋二场在三维空间的辛实现

我们在三个维度上构建了两个相互作用的自旋两个场的动态结构的辛实现。一个显着的简化涉及约束的处理：我们没有像狄拉克那样执行哈密顿分析，而是制定了一种方法，该方法仅使用前辛二形式矩阵及其相应的零模式的性质来研究约束的性质和理论的规范结构。例如，我们证明了具有潜在梯度的零模收缩，产生了对理论动力学的整套约束的明确表达，包括对称化条件以及耦合和宇宙常数之间的明确关系。这条路，我们进一步确定了部分无质量理论的唯一非线性候选者存在的必要条件，仅使用模型相互作用参数的表达式。在规范结构的情况下，整个动态变量集的转换规律更直接地从其余零模式的结构中推导出来；从这个意义上说，零模必须被视为相应规范变换的发生器。此后，我们使用适当的规范固定程序，即时间规范，来计算量化括号和与我们的模型相关的路径积分的功能度量。最后，我们确认三维双重力每个空间点有两个物理自由度。有了以上，