Underlying Pairing States of High $T_c$ Superconductivity

I present a microscopic theory I proposed recently to describe high-T_c superconductivity in cuprates. I show that coherent pairing states consisting of extended singlet Cooper pairs and triplet $\pi$ pairs can manifest both the Mott insulating antiferromagnetic order and the d-wave superconducting order. From this configuration of coherent pairing states, I can describe both the single electron properties and the low energy collective excitations in high T_c superconductivity in the same framework. The quasiparticle can be derived directly with respect to the coherent pairing states. While, the low-lying quantum fluctuations associated with spin-wave and charge excitation can be investigated from the path integral of the coherent pairing states.