  Although one-dimensional systems that exhibit translational symmetry are
generally believed to exhibit anomalous heat transport, previous work has shown
that the model of coupled rotators on a one-dimensional lattice constitute a
possible exception. We investigate the equilibrium spatiotemporal correlations
of energy and momentum of the rotator model, and find that both these fields
diffuse normally. The normal diffusion is explained within the framework of
stochastic hydrodynamics by observing that the angle variables do not
constitute a conserved field, which leads to the absence of long-wavelength
currents in the system. As an outcome of our analysis, we propose some general
criteria for normal transport based on the existence of conservation laws.
