Abstract | The strongly correlated problem in many body physics can be mapped to a weak interacting problem with gauge symmetry. The essential issue for this gauge theory is how to find a gauge fixing condition which is consistent with the local constraint in the strongly correlated system. This was failed in previous studies of the gauge theory. Recently, we developed a consistent gauge theory in the slave boson representation of the strongly correlated fermion system. Using the Faddeev-Popov procedure, the consistent gauge conditions for general gauge theories with Dirac’s first-class constraints were found more than fifty years ago. The BRST symmetry plays a role of the guiding principle in this procedure. We show that it can be used to the strongly correlated system around the atomic limit. But the constraints in the ordered phases of the slave boson representation are Dirac’s second-class ones and so the new method needs to be developed. Fortunately, guided by the BRST symmetry, we established a consistent gauge theory for the ordered phases. Applying to the t-J model, the gauge theory is a theory of the spinon and holon weakly coupled to a dynamic gauge field. We then use Feynman’s diagram technique to perturbatively study the normal state which is believed describing the strange metal physics for the cuprate. Calculations for the other phases such as the pseudogap and superconducting phases are in progress. |
