Quantum theory for the transverse Josephson plasma in high-T_c superconductors

We formulate a quantum theory for the transverse Josephson plasma in intrinsic Josephson junctions. The electromagnetic field is quantized in this formulation. The Josephson plasma is, then, described as the massive photon in superconductors. We derive the transverse dielectric function and calculate the plasma frequency at finite temperatures in the case where the superconducting energy gap has d_{cursive chi 2-y2}-wave symmetry. The effect of thermally excited quasiparticles on the Josephson plasma is discussed. The temperature variation of the plasma frequency near T_c is strongly dependent on the interlayer coupling constants.