Goldilocks Modes and the Three Scattering Bases

Understand

We consider massless scattering from the point of view of the position, momentum, and celestial bases.

• In these three languages different properties of physical processes become manifest or obscured.
• Within the soft sector, they highlight distinct aspects of the infrared triangle: quantum field theory soft theorems arise in the limit of vanishing energy $\omega$, memory effects are described via shifts of fields at the boundary along the null time coordinate $u$, and celestial symmetry algebras are realized via currents that appear at special values of the conformal dimension $\Delta$.
• We focus on the subleading soft theorems at $\Delta=1-s$ for gauge theory $(s=1)$ and gravity $(s=2)$ and explore how to translate the infrared triangle to the celestial basis.