A NEW METHOD TO SHOW THE ABSENCE OF SOME LONG-RANGE ORDERINGS

In this article, we shall show that the correlation function of a loca l operator B(i) decays if there is another local operator A(i) satisfy ing [H, A(i)] = alphaB(i), where H is the Hamiltonian of the many-body system under consideration and alpha is a constant. Finally, as an ap plication of this theorem, we shall rigorously show that the RVB State s, which were proposed by P W Anderson and his collaborators to explai n high-temperature superconductivity, are absent in the Hubbard model at half-filling. We also give an argument, which indicates that the ex istence of the RvB ground states in the doped cases is highly improbab le.