An Explicit Description of the Radiation Field in 3 + 1-dimensions

In previous work with A. Vasy and J. Wunsch, the author established an asymptotic expansion for the radiation field on asymptotically Minkowski spacetimes and showed that the exponents seen in the expansion are given by the poles of a meromorphic family of operators on the spacetime’s “boundary at infinity”. This note provides an explicit accounting of these poles when the spacetime is 3 + 1-dimensional Minkowski space. We conclude by stating the “resonant states” for the first few resonances and then posing a combinatorial problem.