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

Approaching off-diagonal long-range order for 1+1-dimensional relativistic anyons