LAUSR

The criteria for bosonization of Cooper pairs and novel Bose-liquid superconductivity and superfluidity in high-$T_c$ cuprates and other pseudogap matters are formulated by using the uncertainty principle and the boson mean field theory. We argue that the BCS-type s- or d-wave superconductivity occurring in the fermionic limit of Cooper pairs (which exist in ordinary metals and heavily overdoped cuprates with large Fermi energies) is not characteristic of underdoped to overdoped cuprates with low Fermi energies. The superconducting order parameter in high-$T_c$ cuprates and other pseudogap matters cannot be determined as the BCS-like (s- or d-wave) gap. We show that the unconventional superconductivity/superfluidity occurring in the bosonic limit of Cooper pairs exists in low Fermi energy systems where the bosonic Cooper pairs are formed at a pseudogap temperature T* above the uperconducting/superfluid transition temperature $T_c$ and then such bosons condenses into a Bose superfluid at $T_c$. The pair condensation of attracting bosons occurs at $T_c$ and then their single particle condensation sets in at $T_c^*$ lower than $T_c$ (in three dimensions (3D)) or at T=0 (in two dimensions (2D)). The coherent single particle and pair condensates of bosons exist as two distinct superfluid phases below $T_c$. By solving the mean field equations for high-$T_c$ cuprates, the novel superconducting states (i.e., a vortex-like state existing below the temperature $T_v=T^{2D}_c$ lower than T* but higher than $T_c=T^{3D}_c$ and two superconducting phases below $T_c$) and their properties characterized by the boson superfluid stiffness are determined and compared with the key experimental findings. The novel Bose-liquid superconductivity and superfluidity exists also in other exotic superconductors/superfluids, including quantum liquids, atomic Fermi gases and low-density nuclear matter.