无量化、阴影与提升本征函数在洛伦兹AdS中
Null quantization, shadows and boost eigenfunctions in Lorentzian AdS
AI总结：
本文提出AdS中洛伦兹提升本征函数的构造方法，并通过平直空间极限展示其与共形初级波函数的关系。
摘要：
我们重新审视4维洛伦兹反德西特时空（AdS₄）中自由标量的量化问题。我们推导出满足波方程并能在AdS₄的null锥分层中对角化时间平移的解。我们显示，任意质量场的时间平移本征模必须在沿着null叶接近边界时包含可归一化和不可归一化的衰减。然后我们显示AdS bulk-to-boundary传播子在适当的时间顺序下提供波方程的另一种解基。我们提出一个AdS bulk重建公式，将时空点上的自由标量与CFT初级算符及其阴影变换联系起来。在平直空间极限下，该公式退化为平直空间中自由场的Carroll展开。最后我们构建了AdS中在双曲和null分层中的洛伦兹提升本征函数，并显示它们在平直空间极限下分别成为质量为正和零的共形初级波函数。
英文摘要：
We revisit the quantization of a free scalar in 4-dimensional (4d) Lorentzian Anti-de-Sitter spacetime (AdS$_4$). We derive solutions to the wave equation that diagonalize time translations in a foliation of AdS$_4$ with null cones. We show that time-translation eigenmodes of arbitrary mass fields that admit a flat space limit must contain both normalizable and non-normalizable fall-offs as one approaches the boundary along a null leaf. We then show that AdS bulk-to-boundary propagators with suitable time orderings provide alternative bases of solutions to the wave equation. We propose an AdS bulk reconstruction formula relating an on-shell free scalar at a spacetime point to CFT primary operators and their shadow transforms. In the flat space limit, this formula reduces to the Carrollian expansion of a free field in flat space. We finally construct Lorentz boost eigenfunctions in AdS in both hyperbolic and null foliations and show that they respectively become massive and massless conformal primary wavefunctions in the flat space limit.
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