  This paper presents a unified perspective on the results of two recent works
(C. Buragohain and S. Sachdev cond-mat/9811083 and S. Sachdev cond-mat/9810399)
along with additional background. We describe the low frequency, non-zero
temperature, order parameter relaxational dynamics of a number of systems in
the vicinity of a quantum critical point. The dynamical correlations are
properties of the high temperature limit of renormalizable quantum field
theories in spatial dimensions d=1,2. We study, as a function of d and the
number of order parameter components, n, the crossover from the finite
frequency, "amplitude fluctuation", gapped quasiparticle mode in the quantum
paramagnet (or Mott insulator), to the zero frequency "phase" (n>=2) or "domain
wall" (n=1) relaxation mode near the ordered phase. Implications for dynamic
measurements on the high temperature superconductors and antiferromagnetic spin
chains are noted.
