  To supplement our recent brief report on the theory of holon-pair boson
approach to the t-J Hamiltonian [S.-S. Lee and Sung-Ho Suck Salk, Phys. Rev. B
{\bf 64}, 052501(2001)], in this paper we present a full exposure to the
theory, detailed physical implications and predicted various physical
properties of high $T_c$ cuprates. We discuss the significance of coupling
(interplay) between the spin and charge degrees of freedom in the Heisenberg
interaction term of the t-J Hamiltonian. We discuss its importance in causing
the arch-shaped superconducting transition temperature $T_c$ and the pseudogap
(spin gap) temperature $T^*$ tangential to $T_c$ in the overdoped region in the
observed phase diagram of high $T_c$ cuprates. A universal parabolic scaling
behavior of $T^*/T_c$ (or $T_c/T^*$) with hole doping concentration is
predicted in agreement with observations, indicating that there exists
correlation between the pseudogap (spin gap) phase and the superconducting
phase through antiferromagnetic fluctuations. Our proposed holon-pair boson
theory is shown to be self-consistent in that it not only yields the arch
(dome) shape structure of $T_c$ but also reproduces various other physical
properties such as superfluid weight, bose condensation energy, spectral
function, optical conductivity and spin susceptibility, including their
temperature and doping dependence.
