真空涨落谱函数的宏观统计场及其引力意义
A Spectral Criterion for Emergent Gravity
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中文总结 AI 辅助
研究在平坦时空量子场论中引力能否作为能量 - 动量张量真空涨落的宏观统计效应出现。通过动量空间粗粒化等构建宏观张量场，由重整化群不动点控制其动力学，探讨谱极点存在条件及意义，该框架低能极限与广义相对论一致，谱极点问题待检验。
中文摘要 AI 辅助
本文研究了在平坦时空量子场论中，引力作为能量 - 动量张量真空涨落的宏观统计效应出现的可能性。能量 - 动量张量对易子的谱函数作为基本对象，规避了困扰诱导引力方法的真空能量灾难。通过动量空间粗粒化和谱表示，在每个粗粒化尺度上构建了一个宏观对称二阶张量场。粗粒化尺度从外部控制参数提升为动力学序参量。其朗之万动力学由两个重整化群不动点控制：普朗克尺度的紫外排斥点和哈勃尺度的红外吸引点。粗粒化的不可逆性产生了与尺度成反比的有效温度，涨落 - 耗散定理将微观 - 宏观动力学封闭成一个自洽循环。宏观场获得无质量自旋 - 2 传播子的条件是总自旋 - 2 谱密度在零动量处出现孤立极点。微扰理论中不存在此极点，但我们认为在粗粒化流的临界慢化下，它可作为与能量 - 动量张量沃德恒等式兼容的解出现。当极点存在时，温伯格低能定理将非线性自耦合唯一地确定为爱因斯坦 - 希尔伯特作用。牛顿常数和宇宙学常数作为涌现量出现，该框架的低能极限与标准广义相对论一致。谱极点是否实际存在是该框架所依赖的核心问题；原则上可通过晶格规范理论或非微扰泛函重整化群计算进行检验。
英文摘要
We study long-range tensor response and its coupling to matter through sourced spectral equations on fixed spacetime. For a response with a positive spectral representation, the weight at zero is extracted by an infrared limit. At an isolated critical mode, this weight is determined by the propagation slope and the projection of the source onto the critical space. Deriving the kernel and source maps from the same equations allows the residue to be followed through channel elimination and finite approximation. For isolated stationary matter, conservation relates the leading source to the total energy, including interaction contributions. We obtain separate estimates for the potential and force tails under the stated spectral assumptions. Compact spectral examples give explicit endpoint derivatives and tensor overlaps. We also classify the null-shell measure of a covariant stress-tensor realisation. The results provide a criterion for long-range matter exchange, with its gravitational interpretation determined by the tensor structure, coupling and infrared consistency conditions.
发表机构
- Northwestern Polytechnical University（西北工业大学）
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