对“红外引力子能屏蔽$Λ$吗？'
Reply to `Can infrared gravitons screen $Λ$?'
摘要：
最近Garriga和Tanaka对我们的建议提出了批评，即量子引力环修正可能导致有效宇宙学常数的长期屏蔽。他们的论点依赖于重整化方案，其中复合算子$(R \sqrt{-g} - 4 Λ\sqrt{-g} )_{\rm ren}$被定义为重整化场方程的迹。虽然这是一个奇特的处方，我们表明，它{ \it不排除世俗筛选}。此外，我们表明，一个恒定的Ricci标量{ \it甚至不经典}意味着一个恒定的扩展速率。其他要点包括：（1）Garriga和Tanaka的量$R_{\rm ren}$既不是一个适当定义的复合算符，也不是常数;（2）规范依赖性并不使格林函数缺乏物理内容;（3）非动力学de Sitter背景下的标量模型（没有规范问题）可以诱导任意大的长期贡献的应力张量;（4）在量子引力中，同样的长期修正出现在可观测的量中;（5）导出一个简单的量子引力随机公式的前景似乎很好，在这个公式中，主要的长期效应可以求和，甚至复杂的规范不变算符的期望值也可以在主要的阶上计算。
英文摘要：
We reply to the recent criticism by Garriga and Tanaka of our proposal that quantum gravitational loop corrections may lead to a secular screening of the effective cosmological constant. Their argument rests upon a renormalization scheme in which the composite operator $(R \sqrt{-g} - 4 Λ\sqrt{-g} )_{\rm ren}$ is defined to be the trace of the renormalized field equations. Although this is a peculiar prescription, we show that it {\it does not preclude secular screening}. Moreover, we show that a constant Ricci scalar {\it does not even classically} imply a constant expansion rate. Other important points are: (1) the quantity $R_{\rm ren}$ of Garriga and Tanaka is neither a properly defined composite operator, nor is it constant; (2) gauge dependence does not render a Green's function devoid of physical content; (3) scalar models on a non-dynamical de Sitter background (for which there is no gauge issue) can induce arbitrarily large secular contributions to the stress tensor; (4) the same secular corrections appear in observable quantities in quantum gravity; and (5) the prospects seem good for deriving a simple stochastic formulation of quantum gravity in which the leading secular effects can be summed and for which the expectation values of even complicated, gauge invariant operators can be computed at leading order.
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