振幅和Riemann Zeta函数
Amplitudes and the Riemann Zeta Function
摘要：
散射振幅的物理性质映射到黎曼zeta函数。具体地说，一个封闭形式的振幅构造，描述与质量$m_n^2 = μ_n^2$，其中$ζ\left(\frac{1}{2} \pm iμ_n\right) = 0$塔的树级交换。要求真实的质量对应于黎曼假设，振幅的局部性对应于zeta函数的亚纯性，有质量和无质量状态之间的普遍耦合对应于$ζ$的零点的简单性。正向振幅的色散关系的么正性边界转化为$1/μ_n^2$序列的奇阶矩的正性。
英文摘要：
Physical properties of scattering amplitudes are mapped to the Riemann zeta function. Specifically, a closed-form amplitude is constructed, describing the tree-level exchange of a tower with masses $m_n^2 = μ_n^2$, where $ζ\left(\frac{1}{2} \pm iμ_n\right) = 0$. Requiring real masses corresponds to the Riemann hypothesis, locality of the amplitude to meromorphicity of the zeta function, and universal coupling between massive and massless states to simplicity of the zeros of $ζ$. Unitarity bounds from dispersion relations for the forward amplitude translate to positivity of the odd moments of the sequence of $1/μ_n^2$.
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