SEMINAIRE MERCREDI 14 SEPTEMBRE 2005 14 heures Salle Séminaire 5 Centre de Physique Théorique Marseille-Luminy Christian Jaekel Université de Sao Paulo (Brésil) Title: Stability and related properties of vacua and ground states Abstract: We consider the formal non relativistc limit (nrl) of the :\phi^4:_{s+1} relativistic quantum field theory (rqft), where s is the space dimension. We show that (thermodynamic) stability is broken in the formal nrl for s=2, due to the mass renormalization of :\phi^4:_3, despite the fact that (thermodynamic) stability of the full relativistic model holds for both s=1 and s=2. More precisely, we show that for s=2 thermodynamic stability of the nrl is broken for sufficienty large but finite ultarviolet cutoff, due to the infinite mass renormalization of the former theory. In this framework we also compare stability by local perturbations, complete passivity and the existence of local annihilators of the vacuum, for rqft on the one hand, and the formal nrl, on the other. (with Walter Wreszinski)