The sequence of effective theories needed to understand the behavior of real-time correlators (A(t) A(0)) in ultra-relativistic plasmas is discussed. The specific case where A is a gauge-invariant conserved current is considered in detial. Such correlations have been measured in lattice simulations of classical, hot, SU(2)-Higgs gauge theory. simple perturbation theory, free kinetic theory, linearized kinetic theory, and hydrodynamics are all needed to understand the correlation for different ranges of time. It is emphasized that correlations genercially have power-law decay at very large time due to non-linear couplings to long-lived hydrodynamic modes.
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