We introduce a new bosonization technique devised to work in any dimension of space, which makes extensive use of the BRST symmetry. We apply it (successfully) to the problem of re-summing all the non analytic contributions to the thermodynamics of the Landau Fermi liquid theory of metals. This problem, dating from the seminal work of Landau, had been addressed so far only through perturbative expansion in the interactions. We give here its first controlled evaluation through one loop RG.