Unifying soft and hard dynamics: The hard current algebra in celestial holography

Soft current algebras capture the infrared structure of scattering in asymptotically flat spacetimes, but an analogous algebraic description of finite-energy dynamics has been missing. We uncover an infinite-dimensional hard current algebra that encodes finite-energy contributions to scattering and implies novel Ward identities. The soft current algebras are not independent but arise naturally from the hard ones. This provides a unified algebraic framework underlying quantum theory in flat spacetime.