Carrollian Dictionary for Massive Particles at Null Infinity

Abstract

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 Poincar\'e intertwining equations require the complete Carrollian representation to describe massive states. We apply the dictionary to the K\"all\'en--Lehmann representation and to soft photon and graviton theorems. The K\"all\'en--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 Poincar\'e actions, whereas local actions remain integrals over celestial directions.