  We construct and study relativistic anyons in 1+1 dimensions generalizing
well-known models of Dirac fermions. First, a model of free anyons is
constructed and then extended in two ways: (i) by adding density-density
interactions, as in the Luttinger model, and (ii) by coupling the free anyons
to a U(1)-gauge field, as in the Schwinger model. Second, physical properties
of these extensions are studied. By investigating off-diagonal long-range order
(ODLRO) at zero temperature, we show that anyonic statistics allows one to get
arbitrarily close to ODLRO but that this possibility is destroyed by the gauge
coupling. The latter is due to a nonzero effective mass generated by gauge
invariance, which we show also implies the presence of screening, independently
of the anyonic statistics.
