软引力子 $S$-矩阵的引力退相干
Gravitational decoherence from soft-graviton $S$-matrix
- Osaka Central Advanced Mathematical Institute (OCAMI), Osaka Metropolitan University（大阪中央高等数学研究所（OCAMI），大阪公立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文利用软引力子S矩阵推导规范不变的退相干指数，证明真空退相干消失，并分析压缩态及遗迹背景下的增强效应，连接红外量子信息与引力退相干。
AI中文摘要：
我们利用引力子 $S$-矩阵的领头软扇区重新审视物质叠加态的引力退相干。从Weinberg软定理和相干辐射态的重叠出发，对于具有相同总四动量的分支构型，我们推导出一个规范不变、非负的领头软退相干指数，并在此阶精确计算极化求和与角度积分。在真空中，当红外截断被移除时，具有可区分软辐射的分支之间的相干性消失。作为能量-动量守恒的结果，领头非相对论项是纯四极的。我们将分析扩展到单模和双模压缩引力子态，包括受暴胀启发的双模情形。压缩可以增强或抑制退相干，这取决于相对相位，而相位平均则给出由引力子占据数控制的增强。对于在相关软频带上具有近似平坦能量密度谱的相位平均遗迹背景，将红外尺度与观测时间的倒数进行锐截止识别，给出的贡献随引力波能量密度和观测时间的四次方增长。这些结果将软引力子散射、红外量子信息和非真空引力背景中的退相干联系起来。
英文摘要：
We revisit gravitational decoherence of matter superpositions using the leading soft sector of the graviton $S$-matrix. Starting from Weinberg's soft theorem and the overlap of coherent radiation states, we derive, for branch configurations with the same total four-momentum, a gauge-invariant, nonnegative leading-soft decoherence exponent and evaluate the polarization sum and angular integrals exactly at this order. In the vacuum, coherence between branches with distinguishable soft radiation vanishes as the infrared cutoff is removed. The leading nonrelativistic term is purely quadrupolar as a consequence of energy--momentum conservation. We extend the analysis to single- and two-mode squeezed graviton states, including the two-mode case motivated by inflation. Squeezing can enhance or suppress decoherence depending on the relative phase, while phase averaging gives an enhancement governed by the graviton occupation. For a phase-averaged relic background with an approximately flat energy-density spectrum over the relevant soft frequency band, the sharp-cutoff identification of the infrared scale with the inverse observation time gives a contribution that grows with the gravitational-wave energy density and with the fourth power of the observation time. These results connect soft-graviton scattering, infrared quantum information, and decoherence in nonvacuum gravitational backgrounds.
