Influence of Gauge Fluctuation on Electron Pairing Order Parameter and Correlation Functions of a Two-Dimensional System

Based on a two-dimensional electron system with pure gauge field, we demonstrate that the long range order of the electron pairing order parameter can be destroyed by the gauge fluctuation for both s-wave and d-wave symmetric Cooper pair parameters, even if the pure gauge field mediates attractive interaction between the spin-up and spin-down electrons, while the signal of the Meissner effect is observable. This model can be used to explain the recent experimental data of the high T_c cuprate superconductors observed.