arXiv 2302.035472023-02hep-thgr-qc

双曲空间上场的$N$-截断正则化

$N$-cutoff regularization for fields on hyperbolic space

Rudrajit Banerjee, Maximilian Becker, Renata Ferrero

备注：: 35 pages, 1 figure; improved exposition, to appear in PRD

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AI总结：

本文提出背景无关的$N$-截断正则化方案，用于双曲空间上标量场与引力子涨落的自洽量子化，发现无需微调即可避免曲率奇点的宇宙学常数问题，且场模式增多使负曲率趋于零。

摘要：

我们应用一种新颖的背景无关正则化方案，即$N$-截断，对最大对称但非紧致的双曲空间上的标量场和度规涨落进行自洽量子化。对于经典背景上的量子物质场，或在背景场形式论中处理的完整量子爱因斯坦引力（此处视为有效场论），$N$-截断是对场的模式内容的紫外正则化，它独立于背景双曲空间度规。对于每个$N > 0$，正则化系统对几何产生反作用，以动态确定自洽的背景度规。移除正则化的极限随后自动产生所得到的量子场论所赖以存在的“物理正确”时空。当使用$N$-截断进行自洽量子化时，我们发现无需任何参数微调，标量场和（线性化的）引力子场的真空涨落不会导致通常的曲率奇点的宇宙学常数问题。相反，越来越多的场模式的存在倾向于减小双曲空间的负曲率，在移除截断的极限中导致曲率趋于零值。

英文摘要：

We apply a novel background independent regularization scheme, the $N$-cutoffs, to self-consistently quantize scalar and metric fluctuations on the maximally symmetric but non-compact hyperbolic space. For quantum matter fields on a classical background or full Quantum Einstein Gravity (regarded here as an effective field theory) treated in the background field formalism, the $N$-cutoff is an ultraviolet regularization of the fields' mode content that is independent of the background hyperbolic space metric. For each $N > 0$, the regularized system backreacts on the geometry to dynamically determine the self-consistent background metric. The limit in which the regularization is removed then automatically yields the 'physically correct' spacetime on which the resulting quantum field theory lives. When self-consistently quantized with the $N$-cutoff, we find that without any fine-tuning of parameters, the vacuum fluctuations of scalar and (linearized) graviton fields do not lead to the usual cosmological constant problem of a curvature singularity. Instead, the presence of increasingly many field modes tends to reduce the negative curvature of hyperbolic space, leading to vanishing values in the limit of removing the cutoff.

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