Luttinger-liquid phenomenology for high-T-c superconductors

Universal scaling with temperature of the resistivity and optical conductiv ity in the normal state follows from the time-reversal symmetry assumed for the Green function with branch cuts combined with charge-spin separation. The density of states reproduces the extended van Hove singularity in a pla nar system. The single-particle tunneling conductivity in the superconducti ng state is nonzero at zero bias voltage, reproducing the pseudogap charact er of the density of states in the superconducting phase even for the s-wav e symmetry of the order parameter. The form of the Ginzburg-Landau function al is also provided.