四维共形反常、分形时空与精细结构常数
On the four dimensional Conformal Anomaly, Fractal Spacetime and the Fine Structure Constant
摘要：
两年前，安东尼亚迪斯、马祖尔和莫托拉（AMM）在四维引力中量子共形因子的红外固定点处计算了时空的内禀豪斯多夫维数。分维是由高斯-邦尼拓扑项与共形重力异常的系数确定的，并被发现大于4。它明确地表明，如何可以将AMM计算的Hausdorff维数的值与$ϕ^3/2$给出的时空$ε$的普遍维数涨落联系起来，其中$ϕ$是黄金平均值$0.618..$。基于红外标度极限的理论，利用El Naschie最近提出的重整化群论证，我们推测与四维引力共形异常有关的未知系数$Q^2$可以精确地等于逆精细结构常数，其取值范围在$137.036 $ ~ 137.081之间.我们的结果产生的十进制数字的任何$arbitrary$数。
英文摘要：
Antoniadis, Mazur and Mottola (AMM) two years ago computed the intrinsic Hausdorff dimension of spacetime at the infrared fixed point of the quantum conformal factor in 4D Gravity. The fractal dimension was determined by the coefficient of the Gauss-Bonnet topological term associated with the conformal gravitational anomaly and was found to be greater than 4. It is explicitly shown how one can relate the value of the Hausdorff dimension computed by AMM to the universal dimensional fluctuation of spacetime $ε$ given by $ϕ^3/2$, where $ϕ$ is the Golden Mean $0.618..$. Based on the infrared scaling limit of the theory and using recent Renormalization Group arguments by El Naschie, we conjecture that the unknown coefficient $Q^2$, associated with the four dimensional gravitational conformal anomaly, could be precisely equal to the inverse fine structure constant values ranging between $137.036 $ and 137.081. Our results generate decimal digits up to any $arbitrary$ number.
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