An explicit description of the radiation field in 3+1-dimensions

TL;DR

This paper explicitly characterizes the poles of the radiation field in 3+1-dimensional Minkowski space, providing detailed resonance information and posing a related combinatorial problem.

Contribution

It offers an explicit description of the radiation field's poles in 3+1D Minkowski space, building on prior asymptotic expansion results.

Findings

Explicit poles of the radiation field identified

Resonant states for initial resonances described

Poses a combinatorial problem related to resonances

Abstract

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.