Abstract
The effective dynamics of the low-frequency modes is derived for the $O(N)$ symmetric scalar field theory in the broken symmetry phase. The effect of the high-frequency fluctuations is taken into account at one-loop level exactly. A new length scale is shown to govern the long-time asymptotics of the linear response function of the Goldstone modes. The large time asymptotic decay of an arbitrary fluctuation is determined in the linear regime. We propose a set of local equations for the numerical solution of the effective nonlinear dynamics. The applicability of the usual gradient expansion is carefully assessed.
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