U -] INFINITY PROBLEM FOR A FINITE HOLE CONCENTRATION - A BOSONIZATION APPROACH FOR THE NORMAL-STATE HIGH-T(C) SUPERCONDUCTORS

The Hubbard model in the strong coupling limit is considered in two di mensions. A bosonization method based on the extention of the Jordan-W iper transformation to particles with spin and no double occupancy is introduced. We find that at T = 0 a Fermi liquid exists and supercondu ctivity appears. For a finite temperature and finite doping a normal s tate populated with vortices exists. As a result, we have a normal sta te with separated charge- and spin-density-wave excitations. Formally those excitations can be described with the help of the Luttinger-liqu id representation. In the second part we parametrize the Fermi surface by a set of N points. Around each point we describe the Fermi surface excitations by holons and spinons and find a set of N-coupled Lutting er channels. At T = 0 we have space-time tunneling of electric charges which destroys the Luttinger liquid in favor of a Fermi liquid. At T not-equal 0 or LT --> infinity (L is the size of the system) tunneling of electric charges might be prohibited giving rise to gapless excita tions. In the last part we consider the case with a commensurate froze n flux in the ground state. As a result we find that the excitations a re semions.