With the eigen-functional bosonization method, we study one-dimensional strongly correlated electron systems with large momentum (
2kF and/or
4kF) transfer term(s), and demonstrate that this kind of problems ends in to solve the Eikonal-type equations, and these equations are universal, and independent of whether or not the system is integrable. In contrast to usual perturbation theory, this method is valid not only for weak electron interaction, but also for strong electron interaction. Comparing with exact solution of some integrable models, it can give correct results in one-loop approximation. This method can also be used to study electron-phonon interaction systems, and two coupled spin chain or quantum wire systems.
Similar to the bosonization method in one dimension, we divide the electron operators in phase space into two component operators, and study three-dimensional homogeneous electron gas with a strong correlation effect. We apply this method to calculate the pair distribution function g(r = 0, r s ) and the renormalization coefficient of the one-electron Green's function Z(k F ) (Z F ), and show that it has great advantages of succinctness and efficiency for studying one- and three-dimensional systems with a strong correlation effect. This method can be applied to investigate interaction quenches in ultracold atomic gases.