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Using the renormalization method introduced in \cite{GJ}, we prove what we call the {\em local} Boltzmann-Gibbs principle for conservative, stationary interacting particle systems in dimension $d=1$. As applications of this result, we obtain various scaling limits of additive functionals of particle systems, like the occupation time of a given site or extensive additive fields of the dynamics. As a by-product of these results, we also construct a novel process, related to the stationary solution of the stochastic Burgers equation.