论文标题
在渐近安全中的复合算子的缩放上
On the scaling of composite operators in Asymptotic Safety
论文作者
论文摘要
渐近安全假设指出，相互作用的重新归一化组固定点提供了高能重力完成。这意味着对运算符的缩放维度的非平凡量子校正以及相关函数的相关函数，这是相应普遍性类别的特征。我们使用复合算子形式主义进行有效的平均作用，以得出无限几何算子族的缩放维度的分析表达式$ \ int d^dx \ sqrt {g} r^n $。我们证明，当沿重新归一化组轨迹评估时，异常的尺寸在其固定点值和零之间连续插图，该轨迹近似于低能量时经典的一般相对性。因此，当整合量子波动时，就会出现经典的几何形状。我们还将结果与投影到$ f（r）$ - 重力的固定点的稳定性属性进行了比较，这表明单操作员近似中的复合算子形式主义不能用于可靠地确定该理论的相关参数的数量。
The Asymptotic Safety hypothesis states that the high-energy completion of gravity is provided by an interacting renormalization group fixed point. This implies non-trivial quantum corrections to the scaling dimensions of operators and correlation functions which are characteristic for the corresponding universality class. We use the composite operator formalism for the effective average action to derive an analytic expression for the scaling dimension of an infinite family of geometric operators $\int d^dx \sqrt{g} R^n$. We demonstrate that the anomalous dimensions interpolate continuously between their fixed point value and zero when evaluated along renormalization group trajectories approximating classical general relativity at low energy. Thus classical geometry emerges when quantum fluctuations are integrated out. We also compare our results to the stability properties of the interacting renormalization group fixed point projected to $f(R)$-gravity, showing that the composite operator formalism in the single-operator approximation cannot be used to reliably determine the number of relevant parameters of the theory.
