ABSTRACT
This chapter addresses the fundamental role of order parameters and symmetry breaking in characterizing phases and understanding phase transitions and argues that the origin of non-analyticity is in fact the thermodynamic limit. It explores the Landau definition that a transition is first order if the order parameter is discontinuous at the transition point and second order if it is continuous. The chapter presents a general theory which in leading approximation embodies the physics of the Landau function of the order parameter. The mean field theory may be applied quite generally to any system for which the local order parameter has been identified. Once the order parameter for Bose condensation is recognized, the order parameter for superconducting or superfluid transitions follow naturally. For superconducting metals, pairs of electrons at the Fermi surface form bound states which behave effectively as Bosons and thus undergo Bose condensation.
