  The effective theory of low frequency fluctuations of selfinteracting scalar
fields is constructed in the broken symmetry phase. The theory resulting from
integrating fluctuations with frequencies much above the spontanously generated
mass scale $(p_0>>M)$ is found to be local. Non-local dynamics, especially
Landau damping emerges under the effect of fluctuations in the $p_0 \sim M$
region. A kinetic theory of relativistic scalar gas particles interacting via
their locally variable mass with the low frequency scalar field is shown to be
equivalent to this effective field theory for scales below the characteristic
mass, that is beyond the accuracy of the Hard Thermal Loop (HTL) approximation.
