Electrons, pseudoparticles, and quasiparticles in the one-dimensional many-electron problem.

We generalize the concept of quasiparticle for one-dimensional (1D) interacting electronic systems. The ↑ and ↓ quasiparticles recombine the pseudoparticle colors c and s (charge and spin at zero magnetic field) and are constituted by one manypseudoparticle topological momenton and one or two pseudoparticles. These excitations cannot be separated. We consider the case of the Hubbard chain. We show that the low-energy electron – quasiparticle transformation has a singular charater which justifies the perturbative and non-perturbative nature of the quantum problem in the pseudoparticle and electronic basis, respectively. This follows from the absence of zero-energy electron – quasiparticle overlap in 1D. The existence of Fermi-surface quasiparticles both in 1D and three dimensional (3D) many-electron systems suggests there existence in quantum liquids in dimensions 11 or whether it becomes finite as soon as we leave 1D remains an unsolved question.