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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 thehigh-frequency fluctuations is taken into account at one-loop level exactly. Anew length scale is shown to govern the long-time asymptotics of the linearresponse function of the Goldstone modes. The large time asymptotic decay of anarbitrary fluctuation is determined in the linear regime. We propose a set oflocal equations for the numerical solution of the effective non-lineardynamics. The applicability of the usual gradient expansion is carefullyassessed.Comment: 21 pages, LaTeX; final version to appear in Phys. Rev.

Effective theory for the soft fluctuation modes in the spontaneously broken phase of theN-component scalar field theory