There are many special and novel characteristics in high Tc superconductors which do not show in conventional superconductors. One of most peculiar features is the pseudogap. It confuses physicist that why the cuprates go into a gap phase which doesn’t show superconductivity. Recently, many materials are discovered and showing unconventional superconductivity, such as Iron pnictide superconductors and heavy fermion superconductors, which also perform the pseudogap feature. It drives physicist to find out the relation between those materials. In 2014, Prof. Chern considered the pseudogap may be explained by a U(1) gauge field acquiring mass from a Stuckelberg field, which comes from antiferromagnetic fluctuation. In this thesis, I will generalize the abelian system to the non-abelian systems such as SU(2) systems or higher symmetry systems.