1D Generalized Statistics Gas: A Gauge Theory Approach

A field theory with generalized statistics in one space dimension is introduced. The statistics enters the scene through the coupling of the matter fields to a statistical gauge field, as it happens in the Chern-Simons theory in two dimensions. We study the particle-hole excitations and show that the long wavelength physics of this model describes a gas obeying the Haldane generalized exclusion statistics. The statistical interaction is found to provide a way to describe the low-T critical properties of one-dimensional non-Fermi-liquids.