The order parameter for the superconducting phases of UPt3

Abstract I review the principal theories that have been proposed for the superconducting phases of UPt3. The detailed H-T phase diagram places constraints on any theory for the multiple superconducting phases. Much attention has been given to the Ginzberg-Landau region of the phase diagram where the phase boundaries of three phases appear to meet at a tetracritical point. It has been argued that the existence of a tetracritical point for all field orientations eliminates the two-dimensional (2D) orbital representations coupled to a symmetry-breaking field (SBF) as a viable theory of these phases and favours either a theory based on two primary order parameters belonging to different irreducible representations that are accidentally degenerate, as described by Chen and Garg 1993, or a spin-triplet, orbital one-dimensional representation with non spin-orbit coupling in the pairing channel, as described by Machida and Ozaki 1991. I comment on the limitations of the models proposed so far for the superconduct...