The two dimensional Heisenberg antiferromagnet on a square lattice is one of the most studied model quantum magnets. This is in part due to its intrinsic interest but also to the fact that both the cuprates and the pnictide superconductors belong to this class of magnet. In the fully quantum case with s=1/2 an outstanding theoretical and experimental challenge is to understand how the excitations evolve as a function of field. Above a critical field Hc the magnetic moments fully align and the system reduces to a purely classical one, with a quenching of quantum fluctuations. En route to this state it is predicted that the one magnon excitations become unstable due to their interaction with two-magnon states and decay. Here we are proposing to perform a definitive study of this effect which will allow us to test various theoretical scenarios.