Special Public Lecture

The three condensed phases emerging from the GBEC theory in both 2D and in 3D are analyzed and the calculation is sketched of the Helmholtz free energies and their associated critical superconducting temperatures. This is carried out with the boson-fermion interactions switched on and off, and shown to affect critical-temperature values minimally. This implies that most of the physics determining this central property is already included in the zero-order, unperturbed GBEC Hamiltonian. Stability questions are addressed for each of the three condensed phases. The peculiar "background" role played by non-condensed two-hole Cooper pairs is discussed and the ironic fact that it is the two-particle-pair condensate that dominates in the end is emphasized. Empirical evidence from rotating superconducting rings is invoked. Two- to three-order-of-magnitude enhancements in critical temperatures over BCS theory are then possible. Electron-phonon interactions between electrons as used by BCS are shown to suffice in producing high-enough critical temperatures reaching room-temperatures, in principle. But the puzzling role of hole-pairs remains. An effort to understand it better was made by drawing an analogy between hole-pairs and antibosons in the relativistic BEC at temperatures so high that pair production becomes substantial.