The constraint algebra is derived in the second order tetrad Hamiltonian formalism of the bigravity. This is done by a straightforward calculation without involving any insights, implicit functions, and Dirac brackets. The tetrad approach is the only way to present the bigravity action as a linear functional of lapses and shifts and the Hassan–Rosen transform (characterized as ‘a complicated redefinition of the shift variable’ according to the authors) appears here not as an ansatz but as fixing of a Lagrange multiplier. A comparison of this approach with the other ones is provided.

中文翻译：

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四重双引力的约束代数

约束代数以双引力的二阶四阶哈密顿形式导出。这是通过简单的计算完成的，无需涉及任何见解，隐式函数和Dirac括号。四元组方法是将双重力作用表示为偏移和移位的线性函数的唯一方法，而Hassan-Rosen变换（根据作者的描述为“移位变量的复杂重新定义”）在这里不是作为ansatz，而是作为拉格朗日乘数的固定。提供了此方法与其他方法的比较。