The dilute, two-dimensional Bose gas exhibits a novel regime of relaxational
dynamics in the regime k_B T > |\mu| where T is the absolute temperature and
\mu is the chemical potential. This may also be interpreted as the quantum
criticality of the zero density quantum critical point at \mu=0. We present a
theory for this dynamics, to leading order in 1/\ln (\Lambda/ (k_B T)), where
\Lambda is a high energy cutoff. Although pairwise interactions between the
bosons are weak at low energy scales, the collective dynamics are strongly
coupled even when \ln (\Lambda/T) is large. We argue that the strong-coupling
effects can be isolated in an effective classical model, which is then solved
numerically. Applications to experiments on the gap-closing transition of spin
gap antiferromagnets in an applied field are presented.Comment: 9 pages, 10 figure
