arXiv 2107.096012021-07-20gr-qchep-th

牛顿和普朗克的全球动力学

Global Dynamics for Newton and Planck

Alexander Vikman

备注：: Contribution to the 2021 Gravitation session of the 55th Rencontres de Moriond

摘要：

我们讨论最近引入的无标度爱因斯坦方程，其中的信息从他们的跟踪部分丢失。这些方程在经典上等价于广义相对论，但牛顿常数变成了积分常数或全局动力学自由度。因此，从标准量子化的观点来看，这个有效的牛顿常数对量子涨落很敏感。这与单模引力中的宇宙学常数的情况类似，在单模引力中，爱因斯坦方程的迹部分以不同的方式丢失。利用类比的Henneaux-Teitelboim协变作用的么模引力，我们考虑不同的一般协变作用导致这些动态。这种设置允许一个制定海森堡不确定性关系的牛顿常数和正则共轭量。出乎意料的是，其中一个理论还将普朗克量子常数提升到了一个受量子涨落影响的全局自由度。在与单模引力类比之后，我们讨论了描述无标度爱因斯坦方程的非协变的“单物质”和“单曲率”引力。最后，我们证明了在杨-米尔斯规范理论的某些限制下，“冻结”类轴子场可以模拟引力牛顿常数，甚至量子普朗克常量。

英文摘要：

We discuss recently introduced scale-free Einstein equations, where the information from their trace part is lost. These equations are classically equivalent to General Relativity, yet the Newton constant becomes a constant of integration or a global dynamical degree of freedom. Thus, from the point of view of standard quantization, this effective Newton constant is susceptible to 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. Using analogy with the Henneaux-Teitelboim covariant action for the unimodular gravity, we consider different general-covariant actions resulting in these dynamics. This setup allows one to formulate the Heisenberg uncertainty relations for the Newton constant and canonically conjugated quantities. Unexpectedly, one of such theories also promotes the Planck's quantum constant to a global degree of freedom, which is subject to quantum fluctuations. Following analogy with the unimodular gravity, we discuss non-covariant "unimatter" and "unicurvature" gravities describing the scale-free Einstein equations. Finally, we show that in some limit of the Yang-Mills gauge theory a "frozen" axion-like field can emulate the gravitational Newton constant or even of the quantum Planck constant.

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