零无穷远处有质量粒子的Carrollian字典
Carrollian Dictionary for Massive Particles at Null Infinity
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中文总结 AI 辅助
本研究构建了适用于零无穷远上有质量单粒子态的Carrollian字典，无需粒子世界线抵达零无穷远，通过体动量在零标架的投影编码体动量，将其应用于Källén–Lehmann表示与软定理，明确了相关系数与作用形式，完善了有质量粒子的Carrollian边界描述。
中文摘要 AI 辅助
有质量粒子抵达类时无穷远而非零无穷远，这使得它们的Carrollian边界描述尚未得到解决。我们构建了适用于$\boldsymbol{\text{I}}^\boldsymbol{\text{±}}$上有质量单粒子态的Carrollian字典，无需要求这些粒子的世界线抵达零无穷远。该字典通过体动量在与每个天点相关的零标架上的投影来编码体动量。庞加莱（Poincaré）缠结算子方程要求完整的Carrollian表示来描述有质量态。我们将该字典应用于Källén–Lehmann表示以及软光子和软引力子定理。Källén–Lehmann应用依据体谱密度确定了非接触两点函数的系数函数。软定理表明，全局模式可复现普通的U(1)和庞加莱作用，而局域作用仍为天球方向上的积分。
英文摘要
Massive particles reach timelike rather than null infinity, leaving their Carrollian boundary description unresolved. We construct a Carrollian dictionary for massive one-particle states on $\mathscr I^\pm$ without requiring their worldlines to reach null infinity. The dictionary encodes the bulk momentum through its projections onto the null frame associated with each celestial point. The Poincaré intertwining equations require the complete Carrollian representation to describe massive states. We apply the dictionary to the Källén--Lehmann representation and to soft photon and graviton theorems. The Källén--Lehmann application fixes the coefficient function of the non-contact two-point function in terms of the bulk spectral density. Soft theorems show that global modes reproduce the ordinary $U(1)$ and Poincaré actions, whereas local actions remain integrals over celestial directions.
