We show that promoting the trace part of the Einstein equations to a trivial identity results in the Newton constant being an integration constant. Thus, in this formulation the Newton constant is a global dynamical degree of freedom which is also a subject to quantization and quantum fluctuations. This is similar to what happens to the cosmological constant in the unimodular gravity where the trace part of the Einstein equations is lost in a different way. We introduce a constrained variational formulation of these modified Einstein equations. Then, drawing on analogies with the Henneaux-Teitelboim action for unimodular gravity, we construct different general-covariant actions resulting in these dynamics. The inverse of dynamical Newton constant is canonically conjugated to the Ricci scalar integrated over spacetime. Surprisingly, instead of the dynamical Newton constant one can formulate an equivalent theory with a dynamical Planck constant. Finally, we show that an axion-like field can play a role of the gravitational Newton constant or even of the quantum Planck constant.

我们表明，将爱因斯坦方程的迹部分提升为平凡恒等式会导致牛顿常数成为积分常数。因此，在这个公式中，牛顿常数是一个全局动态自由度，它也是量子化和量子涨落的主题。这类似于单模引力中的宇宙常数发生的情况，其中爱因斯坦方程的迹线部分以不同的方式丢失。我们介绍了这些修改后的爱因斯坦方程的约束变分公式。然后，通过与 Henneaux-Teitelboim 作用的类比，我们构建了不同的通用协变作用，从而产生了这些动力学。动力学牛顿常数的倒数与时空积分的 Ricci 标量典型地共轭。出奇，代替动力学牛顿常数，可以用动力学普朗克常数制定等效理论。最后，我们证明了类轴子场可以发挥引力牛顿常数甚至量子普朗克常数的作用。