  We consider the Hubbard chain in a magnetic field and chemical potential. We
introduce a pseudohole basis where all states are generated from a single
reference vacuum. This allows the evaluation for all sectors of Hamiltonian
symmetry of the model of the expression of the $\sigma $ electron and hole
operators at Fermi momentum $\pm k_{F\sigma }$ and vanishing excitation energy
in terms of pseudohole operators. In all sectors and to leading order in the
excitation energy the electron and hole are constituted by one $c$ pseudohole,
one $s$ pseudohole, and one {\it topological momenton}. These three quantum
objects are confined in the electron or hole and cannot be separated. We find
that the set of different pseudohole types which in pairs constitute the two
electrons and two holes associated with the transitions from the $(N_{\uparrow
}, N_{\downarrow })$ ground state to the $(N_{\uparrow }+1,N_{\downarrow })$,
$(N_{\uparrow },N_{\downarrow }+1)$ and $(N_{\uparrow }-1, N_{\downarrow })$,
$(N_{\uparrow },N_{\downarrow }-1)$ ground states, respectively, transform in
the representation of the symmetry group of the Hamiltonian in the
initial-ground-state sector of parameter space. We also find the pseudohole
generators for the half-filling holon and zero-magnetic-field spinon. The
pseudohole basis introduced in this paper is the only suitable for the
extension of the present type of operator description to the whole Hilbert
space.
