Pion and Kaon Condensation at Finite Temperature and Density
  In this paper, we study O(2N)-symmetric $\phi^4$-theory at finite temperature and density using the 2PI-1/N expansion. As specific examples, we consider pion condensation at finite isospin chemical potential and kaon condensation at finite chemical potential for hyper charge and isospin charge. We calculate the phase diagrams and the quasiparticle masses for pions and kaons in the large-N limit. It is shown that the effective potential and the gap equation can be renormalized by using local counterterms for the coupling constant and mass parameter, which are independent of temperature and chemical potentials. 
Jens O. Andersen