In relativistic heavy ion collisions large numbers of pions are created. It may be possible for these pions to condense into the zero-momentum state, i.e. form a Bose-Einstein condensate. Pions have the special property of being Goldstone bosons of the spontaneously broken chiral symmetry of QCD. The O(N)-symmetric linear sigma model is used as an effective low energy model for QCD to understand the relationship between chiral symmetry breaking and Bose-Einstein condensation. This has recently been studied by Shu and Li and by Andersen. Shu and Li use the framework of the Cornwall-Jackiw-Tomboulis formalism and the 1/N approximation, while Andersen uses the 2PI (Phi derivable) method. I will review their work and attempt to go further in understanding the thermodynamic properties of the sytem.
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