论文标题
de安慰剂空间中耦合标量场的应力张量的点拆分正规化
Point-splitting regularization of the stress tensor of a coupling scalar field in de Sitter space
论文作者
论文摘要
我们根据绝热绿色功能的指导，在DE Sitter空间中的耦合标量场的真空应力张量上进行点拆分正则化。对于具有最小耦合$ξ= 0 $的巨大标量场，第二阶分解正则化会产生有限的真空应力张量，其正恒能密度为正，可以识别为宇宙学常数，可驱动DE Sitter膨胀。对于耦合$ξ\ ne 0 $，我们发现，即使正则化绿色的函数是连续的，紫外线和IR收敛的，点拆分正则化也不会自动导致适当的应力张量。耦合$ξr$会导致日志发散项，以及取决于巧合极限路径的高阶术语。在通过额外处理删除了这些不必要的术语后，小耦合$ξ\ in（0，\ frac {1} {7.04}）$的二阶正规化分别是$ξ= \ frac16 $的子顺式插入的0级正规化，产生了$ parecy $ nituite $ beation $ nitunite $ beation $ $ nitune $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $。对于具有$ξ= 0 $或$ξ= \ frac16 $的无质量场，点拆分正则化会产生消失的真空应力张量，并且没有$ξ= \ frac16 $的共形痕量痕量异常。如果采取了第四阶正规化，则一般$ξ$的正则能量密度为负，这与DE Sitter通货膨胀不一致，并且正则化绿色的功能将在零质量上是单数，这是毫无态的。在所有这些情况下，分类正则化的应力张量等于绝热的正则化。
We perform the point-splitting regularization on the vacuum stress tensor of a coupling scalar field in de Sitter space under the guidance from the adiabatically regularized Green's function. For the massive scalar field with the minimal coupling $ξ=0$, the 2nd order point-splitting regularization yields a finite vacuum stress tensor with a positive, constant energy density, which can be identified as the cosmological constant that drives de Sitter inflation. For the coupling $ξ\ne 0$, we find that, even if the regularized Green's function is continuous, UV and IR convergent, the point-splitting regularization does not automatically lead to an appropriate stress tensor. The coupling $ξR$ causes log divergent terms, as well as higher-order finite terms which depend upon the path of the coincidence limit. After removing these unwanted terms by extra treatments, the 2nd-order regularization for small couplings $ξ\in(0,\frac{1}{7.04})$, and respectively the 0th-order regularization for the conformal coupling $ξ=\frac16$, yield a finite, constant vacuum stress tensor, in analogy to the case $ξ=0$. For the massless field with $ξ=0$ or $ξ=\frac16$, the point-splitting regularization yields a vanishing vacuum stress tensor, and there is no conformal trace anomaly for $ξ=\frac16$. If the 4th-order regularization were taken, the regularized energy density for general $ξ$ would be negative, which is inconsistent with the de Sitter inflation, and the regularized Green's function would be singular at the zero mass, which is unphysical. In all these cases, the stress tensor from the point-splitting regularization is equal to that from the adiabatic one.
