Quantum theory for the longitudinal Josephson plasma in high-T_c superconductors: QED in 1D Josephson junction array

We present a new microscopic theory based on the quantum electrodynamics for the longitudinal Josephson plasma in strongly anisotropic high-T_c superconductors. The longitudinal electric field is quantized in terms of the phason gauge in which the phason velocity is sell-consistently determined. The longitudinal photon propagator is calculated within the 2nd order tunneling process from which the Josephson effect arises. The longitudinal dielectric function is also derived. The dispersion relation and the temperature dependence of the longitudinal Josephson plasma propagating in the direction of the layer stacking is calculated from the dielectric function. It is predicted that the Josephson plasma frequency vanishes at T_c in the case where the interlayer coupling constant is less than some critical value.