  Using eigen-functional bosonization method, we study quantum many-particle
systems, and show that the quantum many-particle problems end in to solve the
differential equation of the phase fields which represent the particle
correlation strength. Thus, the physical properties of these systems are
completely determined by the differential equation of the phase fields. We
mainly focus on the study of D-dimensional electron gas with/without transverse
gauge fields, two-dimensional electron gas under an external magnetic field,
D-dimensional boson systems, a D-dimensional Heisenberg model and a one-band
Hubbard model on a square lattice, and give their exact (accurate for
Heisenberg model) functional expressions of the ground state energy and action,
and the eigen-functional wave functions of the fermions/bosons. With them, we
can calculate a variety of correlation functions of the systems, such as single
particle Green's functions and their ground state wave functions. In present
theoretical framework, we can unifiably represent the Landau Fermi liquid,
non-Fermi liquid ($D\geq 2$) and Tomonaga-Luttinger liquid.
