论文标题
零频率重力的角动量
Angular momentum of zero-frequency gravitons
论文作者
论文摘要
通过遵循Weinberg的软定理，该定理捕获了$ 1/ω$极点在任意背景硬过程的基础上，对软重力排放的振幅（$ω<λ$）的振幅贡献，我们计算了Graviton Angular Momentum Operator的期望值，以使其与软辐射的任意碰撞装饰。我们发现结果变得独立于重力频率的截止$λ$，有效地定位在$ω= 0 $。这样，我们的结果捕获了对零频模式的角动量的贡献。像软定理一样，我们的公式对硬粒子的运动学具有准确的依赖性，并且只是其动量的函数。例如，我们详细讨论了$ 2 \至2 $在一般相对论和$ {\ cal n} = 8 $ supergravity中散射的$ 2 \ 2 $。
By following closely Weinberg's soft theorem, which captures the $1/ω$ pole contribution to the amplitude for soft graviton emissions ($ω<Λ$) on top of an arbitrary background hard process, we calculate the expectation value of the graviton's angular momentum operator for arbitrary collisions dressed with soft radiation. We find that the result becomes independent of the cutoff $Λ$ on the graviton's frequency, effectively localizing at $ω=0$. In this way, our result captures the contribution to the angular momentum that comes from the zero-frequency modes. Like the soft theorem, our formula has an exact dependence on the kinematics of the hard particles and is only a function of their momenta. As an example, we discuss in some detail the case of the $2 \to 2$ scattering of spinless particles in General Relativity and ${\cal N}=8$ supergravity.
