The recent observation of Bose–Einstein condensation in a polarised alkaline gas is of major significance to the content of this book. Although opinions may differ as to the significance of the observation itself to the physics, everybody must have applauded the impressive success achieved by the novel techniques. Thanks to the discovery which provided us with concrete examples of a dilute Bose gas discussed in Section 1.2, the macroscopic quantum wave function, the central concept in understanding superconductivity and superfluidity, now seems quite familiar to us. Although this subject has been treated in the Appendix of [E-11], we will briefly discuss it here from the viewpoint of the physics of the condensate. We hope that this is read together with the Appendix of [E-11].

The Nobel prize in physics for 1996 was awarded to D.D. Osheroff, R.C. Richardson and D.M. Lee for the discovery of superfluid 3He. The research on superfluidity due to 3P pairing, initiated by this discovery, taught us that the physics of pairing is quite rich. The lessons learned here have been helpful in research on high temperature superconductors, heavy electron systems and, moreover, superconductivity in hadronic matter.

One of the interesting developments in the research on HTSC is an attempt to observe directly the pairing type, now considered likely to be d. This will be discussed in Appendix A2.1. Another unique example of the physics of HTSC is its behaviour in a magnetic field, involving vortex lattice, vortex liquid and glass.