  In this letter we study 1+1 anyon fields at finite temperature and density
with non-vanishing chemical potentials. Our approach is based on an operator
formalism for bosonization at finite temperature; the correlation functions for
the system are given in an explicit form. Two are the main results of this
construction: we point out the existence of persistent currents in 1+1 anyon
systems; from the analysis of 2-point anyon field correlation function, a
remarkable and new condensation phenomenon in momentum space is discovered. As
a concrete example, the above formalism is applied to the Thirring model.
