解析延拓的危险
The Perils of Analytic Continuation
摘要：
莫里森的一篇很好的论文证明了最近关于德西特背景下引力子传播子的观点的趋同。我们在这里讨论仍有争议的几点。首先，快子标量的不可避免的衰变确实会导致它们的2点函数打破德西特不变性。这是模糊的解析延拓技术，产生正式的解决方案，传播方程，而不是传播。第二，Morrison的de Sitter不变量解的自旋2扇区的引力子传播涉及的标量传播$M^2 = 0$的衍生物，它不是亚纯的，除非de Sitter破坏是允许的。第三，德西特破缺不需要零模。第四，莫里森在自旋二结构函数的方程中声称的模糊性通过要求它从模和导出而被固定。第五，莫里森的自旋二扇区与我们的扇区并不“物理等价”，因为它们的重合极限不同。最后，只有非不变传播子才能正确地得到张量功率谱的时间无关性和尺度不变性。
英文摘要：
A nice paper by Morrison demonstrates the recent convergence of opinion that has taken place concerning the graviton propagator on de Sitter background. We here discuss the few points which remain under dispute. First, the inevitable decay of tachyonic scalars really does result in their 2-point functions breaking de Sitter invariance. This is obscured by analytic continuation techniques which produce formal solutions to the propagator equation that are not propagators. Second, Morrison's de Sitter invariant solution for the spin two sector of the graviton propagator involves derivatives of the scalar propagator at $M^2 = 0$, where it is not meromorphic unless de Sitter breaking is permitted. Third, de Sitter breaking does not require zero modes. Fourth, the ambiguity Morrison claims in the equation for the spin two structure function is fixed by requiring it to derive from a mode sum. Fifth, Morrison's spin two sector is not "physically equivalent" to ours because their coincidence limits differ. Finally, it is only the noninvariant propagator that gets the time independence and scale invariance of the tensor power spectrum correctly.
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