论文标题
非最小$ ϕ^2 r $耦合和重力接触互动的重新归一化组
Renormalization Group for Non-minimal $ϕ^2 R$ Couplings and Gravitational Contact Interactions
论文作者
论文摘要
标量和重力的理论，具有爱因斯坦 - 希尔伯特项和非最小相互作用，$ m^2r/2-αϕ^2R/12 $具有重力交换引起的接触相互作用。这些修改了重新归一化组，从而导致约旦框架中常规计算之间的差异忽略了这种效果（并且发现不正确），而$α$的爱因斯坦框架不存在。因此，约旦和爱因斯坦框架中量子效应的计算通常与从约旦到爱因斯坦框架的过渡通常不会通勤。在爱因斯坦的框架中，尽管没有$α$，但对于规模的小步骤$Δμ$ $ $ $ $ $ $ $ $ \simΔα$是诱导的，然后通过接触项将其吸收到其他耦合中。这修改了爱因斯坦框架中的$β$ - 功能。我们通过包含此效果来展示如何在简单模型中获得正确的结果。
Theories of scalars and gravity, with an Einstein-Hilbert term and non-minimal interactions, $M^2R/2 -αϕ^2R/12 $, have graviton exchange induced contact interactions. These modify the renormalization group, leading to a discrepancy between the conventional calculations in the Jordan frame that ignore this effect (and are found to be incorrect), and the Einstein frame in which $α$ does not exist. Thus, the calculation of quantum effects in the Jordan and Einstein frames does not generally commute with the transition from the Jordan to the Einstein frame. In the Einstein frame, though $α$ is absent, for small steps in scale $δμ/μ$ infinitesimal contact terms $\sim δα$ are induced, that are then absorbed back into other couplings by the contact terms. This modifies the $β$-functions in the Einstein frame. We show how correct results can be obtained in a simple model by including this effect.
