Abstract: The hydrogen atom in the Stark effect and Zeeman effect is mapped into the four-dimensional anisotropican harmonic oscillator by the Green function. The Symmetry Factor of four loops Vacuum Diagram is given. The tensor of Multicomponent4field is introduced to calculate the new case of Multicomponent42 field in the Zeeman effect. The four-order perturbation expansion of the ground state is studied by the mean of Multicomponent Field Symmetry Factor and Feynman Diagram. The4-theory may be the new tool for the study of Coulomb system.