AI 中文总结
该研究基于广义相对论预正则化量子化的量子自旋连接泡沫，修正牛顿动力学得到符合MOND的加速度标度，还关联了宇宙学常数，其效应或可在太阳系及实验室观测。
AI 中文摘要
我们认为，根据广义相对论的预正则化量子化所描述的量子引力的量子自旋连接泡沫效应，可能已通过小宇宙学常数和小加速度下牛顿动力学的修正形式被观测到，这种修正表现为星系的平坦旋转曲线。我们得到了考虑基本小加速度标度$a_* = 8\pi G\hbar\varkappa$的牛顿势修正，其中$\varkappa$是具有空间体积倒数量纲的参数，其出现基于量纲分析。$\varkappa$与标准模型纯杨-米尔斯部分质量隙的强子标度之间的关联，使$a_*$的估计值与MOND中的Milgrom加速度标度相符；$a_*^2$与宇宙学常数的关联则给出了符合实际的宇宙学常数值。在经典动力学被预正则化量子引力非相对论近似下最简解计算得到的平均场加速度修正的假设下，我们导出了具有理论上不同插值函数的Milgromian MOND。我们还指出，经自旋连接泡沫修正的牛顿动力学效应可能在太阳系甚至实验室实验中被观测到。
英文摘要
We argue that effects of the quantum spin-connection foam, which describes quantum gravity according to the precanonical quantization of General Relativity, may already be observed in the form of the small cosmological constant and a modification of Newtonian dynamics at small accelerations, manifested in the flat rotation curves of galaxies. We obtain a modification of the Newtonian potential that takes into account the existence of a fundamental small acceleration scale, $a_* = 8πG\hbar\varkappa$, where $\varkappa$ is a parameter with the dimensions of inverse spatial volume that appears on dimensional grounds. The connection between $\varkappa$ and the hadronic scale of the mass gap in the pure Yang-Mills sector of the Standard Model leads to an estimated value of $a_*$ compatible with the Milgromian acceleration scale in MOND. The connection between $a_*^2$ and the cosmological constant leads to a realistic value of the latter. Milgromian MOND, together with a theoretically distinct interpolating function, is derived under the assumption that classical dynamics is modified by the mean-field acceleration calculated from the simplest solution of precanonical quantum gravity in the nonrelativistic approximation. We also indicate that the effects of Newtonian dynamics modified by the spin-connection foam may be observable in the Solar System and even in laboratory experiments.
Comments17 pages. To appear in: The Seventeenth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories, Pescara 7-12 July 2024, edited by G. Vereshchagin and R. Ruffini, https://doi.org/10.1142/14814, October 2026. Corrects typos in eqs (26), (29) in the published version, adds refs [64-66]
