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Dealing with ghost-free massive gravity without explicit square roots of matrices

机译:处理无鬼的大重力而无需明确的矩阵平方根

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In this paper we entertain a simple idea that the action of ghost free massive gravity (in metric formulation) depends not on the full structure of the square root of a matrix but rather on its invariants given by the elementary symmetric polynomials of the eigenvalues. In particular, we show how one can construct the quadratic action around Minkowski spacetime without ever taking the square root of the perturbed matrix. The method is however absolutely generic. And it also contains the full information on possible non-standard square roots coming from intrinsic non-uniqueness of the procedure. In passing, we mention some hard problems of those apocryphal square roots in the standard approach which might be better tackled with our method. The details of the latter are however deferred to a separate paper.
机译:在本文中,我们得出一个简单的想法,即无鬼影的大重力(以公制表示)的作用不取决于矩阵平方根的完整结构,而取决于特征值的基本对称多项式给出的不变量。特别是,我们展示了如何能够在不考虑扰动矩阵的平方根的情况下构造围绕Minkowski时空的二次动作。但是,该方法绝对是通用的。并且还包含有关该过程的固有非唯一性可能的非标准平方根的完整信息。顺便说一句,我们在标准方法中提到了那些伪骨方根的一些难题,这些难题可能可以用我们的方法更好地解决。但是,后者的详细信息将推迟到另一篇论文中。

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