论文标题
分数软限制
Fractional soft limits
论文作者
论文摘要
涉及一个软nambu的散射过程的振幅是一个常见的知识 - 戈尔德石玻色子应像软动量的整数能力一样缩放。我们通过考虑固体中声子的$ 2 \ 2 $散射来重新审视这一期望。我们表明，根据散射过程中涉及的声子的螺旋性，散射幅度实际上可能像软动量的分数能力一样消失。这是4点振幅的特殊性，可以追溯到（1）Lorentz不变性的（自发或显式）破裂，以及（2）当一个声子变成软的声子时，会产生的近似界线动力学。我们的结果扩展到了向量领域的非偏见性转移不变理论的一般类别。
It is a common lore that the amplitude for a scattering process involving one soft Nambu--Goldstone boson should scale like an integer power of the soft momentum. We revisit this expectation by considering the $2 \to 2$ scattering of phonons in solids. We show that, depending on the helicities of the phonons involved in the scattering process, the scattering amplitude may in fact vanish like a fractional power of the soft momentum. This is a peculiarity of the 4-point amplitude, which can be traced back to (1) the (spontaneous or explicit) breaking of Lorentz invariance, and (2) the approximately collinear kinematics arising when one of the phonons becomes soft. Our results extend to the general class of non-relativistic shift-invariant theories of a vector field.
