U(1) Gauge Theory as a Collective Field Theory for Hubbard Model

Abstract

I construct a collective field theory for Hubbard model of high Tc superconductivity, using a path-integral method in the third quantized (slave boson) form. It is a U(1) gauge invariant theory consisting of a U(1) gauge field and a Higgs scalar. The gauge field stands for resonating valence bonds and describes a (short range) antiferro-paramagnet phase transition by a condensation machanism. The Higgs scalar represents spinless holes carrying electric charges. Through the confining gauge force, there formed bounded hole pairs on each link, which correspond to the vector mesons in lattice QCD. A superconducting phase is to be described by a condensation of a gauge invariant order parameter for these hole pairs, and to be compared with the color confining chirally broken phase in QCD. A Ginzburg-Landau theory for the vector hole-pair field is proposed.