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A non-perturbative s-wave renormalization of the pion in a hot and baryonrich medium is presented. This approach proceeds via a mapping of the canonicalpion into the axial Noether's charge. The mapping was made dynamical in theHartree-Fock-Bogoliubov random phase approximation (HFB-RPA). It is shown thatthis approach, while order mixing, is still symmetry conserving both in thebaryon free and baryon rich sectors, at zero as well as finite temperature. Thesystematic character of this approach is emphasized and it is particularlyargued that it may constitute an interesting alternative for thenon-perturbative assessment of the nuclear matter saturation properties.Comment: Latex, 22 pages, 3 figure

Symmetry conserving nonperturbatives-wave renormalization of the pion in a hot and baryon-dense medium