论文标题
在三个维度上两个相互作用的自旋两场场的符号实现
Symplectic realization of two interacting spin-two fields in three dimensions
论文作者
论文摘要
我们在三个维度上构建了两个相互作用的自旋两场场的动态结构的符合性实现。大量简化是指处理约束：而不是执行哈密顿分析$ \ grave {a} \，la $ dirac，我们制定了一种方法，它仅使用一种使用前隔离的两种形式矩阵的属性及其相应的零模型来研究理论的约束性质和规范结构的性质。例如，我们证明了零模型与潜在梯度的收缩，对理论动力学的整个约束产生明确的表达，包括对称条件和耦合和宇宙常数之间的明确关系。这样，我们进一步确定了仅使用模型相互作用参数的表达式来确定存在独特的非线性候选者的必要条件。在量规结构的情况下，整个动力学变量集的转换定律更直接地从剩余的零模型的结构中得出。从这个意义上讲，零模型必须被视为相应仪表转换的发生器。此后，我们使用适当的量规程序时间表来计算与模型相关的路径积分上的量化括号和功能度量。最后，我们确认三维双重野兽具有每个空间点的两个物理自由度。在上述情况下，我们提供了一个新的观点，可以更好地理解相互作用的旋转两个场理论的动态结构，而这种结构不需要像Dirac的标准方法那样将约束作为一流和二等阶段的约束。
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 $\grave{a}\, la$ 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.
