Pion condensates

We review recent developments which indicate that neutron or nuclear matter at sufficiently high density undergoes a phase transition into a pion condensate. Following an introductory discussion of the simplest possible models, realistic features are added stepwise, like the role of short-range nucleon-nucleon correlations and the importance of the Δ(1230) isobar. Results of realistic calculations of the critical density for pion condensation in neutron matter are summarized, which show that the phase transition appears around or beyond twice the density of nuclear matter. In the last three sections we summarize the description of pion condensation within the framework of the sigma model, based on chiral symmetry, and generalized to include short-range correlations and Δ(1230) isobars. This model permits one to construct the equation of state for pion condensed neutron matter. The presence of a pion condensate generally leads to a softening of the equation of state. Some implications on the structure of neutron stars are studied in the final section.