TOPOLOGICAL GROUND-STATE EXCITATIONS AND SYMMETRY IN THE MANY-ELECTRON ONE-DIMENSIONAL PROBLEM

We consider the Hubbard chain in a magnetic field and chemical potenti al. We introduce a pseudohole basis where all states are generated fro m a single reference vacuum. This allows the evaluation for all sector s of hamiltonian symmetry of the model of the expression of the sigma electron and hole operators at Fermi momentum +/-k(F sigma) and vanish ing excitation energy in terms of pseudohole operators. In all sectors and to leading order in the excitation energy the electron and hole a re constituted by one c pseudohole, one s pseudohole, and one topologi cal momenton. These three quantum objects are confined in the electron or hole and cannot be separated. We find that the set of different ps eudohole types which in pairs constitute the two electrons and two hol es associated with the transitions from the (N up arrow, N down arrow) ground state to the (N up arrow + 1, N down arrow), (N up arrow, N do wn arrow + 1) and (N up arrow - 1, N down arrow), (N up arrow, N down arrow - 1 ) ground states, respectively, transform in the representati on of the symmetry group of the hamiltonian in the initial-ground-stat e sector of parameter space. We also find the pseudohole generators fo r the half-filling holon and zero-magnetic-field spinon. The pseudohol e basis introduced in this paper is the only suitable for the extensio n of the present type of operator description to the whole Hilbert spa ce.