Quantum phase transitions have recently received a lot of interest in various different fields of physics and the emergent universal properties have been studied in very different systems. Examples include 2D electron gases in semiconductor heterostructures, superfluid- or metal-insulator transitions, non-Fermi liquid behaviors or the condensation of quasi-particles in magnetic insulators. In our experiment we propose to study one particular field induced quantum critical point in a quasi-two-dimensional quantum magnet by means of inelastic neutron scattering. For the particular quantum critical point under study, d=2 corresponds to the upper critical dimension. Thus, the proposed experiment will allow as to study in detail quantum critical dynamics at the upper critical dimension.