Title: Generalization of the Fierz-Pauli Action Show Chinese title

Title: Fierz-Pauli作用量的推广

Abstract: We consider the Lagrangian of gravity covariantly amended by the mass and polynomial interaction terms with arbitrary coefficients, and reinvestigate the consistency of such a theory in the decoupling limit, up to the fifth order in the nonlinearities. We calculate explicitly the self-interactions of the helicity-0 mode, as well as the nonlinear mixing between the helicity-0 and -2 modes. We show that ghost-like pathologies in these interactions disappear for special choices of the polynomial interactions, and argue that this result remains true to all orders in the decoupling limit. Moreover, we show that the linear, and some of the nonlinear mixing terms between the helicity-0 and -2 modes can be absorbed by a local change of variables, which then naturally generates the cubic, quartic, and quintic Galileon interactions, introduced in a different context. We also point out that the mixing between the helicity-0 and 2 modes can be at most quartic in the decoupling limit. Finally, we discuss the implications of our findings for the consistency of the effective field theory away from the decoupling limit. Show Chinese abstract

Abstract: 我们考虑通过质量项和多项式相互作用项以协变方式修正的引力拉格朗日量，其系数为任意值，并重新研究该理论在解耦极限下的一致性，直到非线性项的第五阶。 我们明确计算了自旋-0模的自相互作用，以及自旋-0模和自旋-2模之间的非线性混合。 我们表明，对于多项式相互作用的特殊选择，这些相互作用中的类似鬼态的问题会消失，并且我们认为这一结果在解耦极限下对所有阶数都成立。 此外，我们表明自旋-0模和自旋-2模之间的线性以及一些非线性混合项可以通过局部变量变换吸收，这自然产生了在不同背景下引入的三次、四次和五次伽利略相互作用。 我们还指出，在解耦极限下，自旋-0模和2模之间的混合最多是四次的。 最后，我们讨论了我们的发现对远离解耦极限的有效场论一致性的意义。