  We study bosonisation in the massive Thirring and sine-Gordon models at
finite temperature and nonzero fermion chemical potential. Both canonical
operator and path integral approaches are used to prove the equality of the
partition functions of the two models at finite $T$ and zero chemical
potential, as it has been recently shown. This enables the relationship between
thermal normal ordering and path-integral renormalisation to be specified.
Furthermore, we prove that thermal averages of zero-charge operators can also
be identified. At nonzero chemical potential and temperature we show, in
perturbation theory around the massless case, that the bosonised theory is the
sine-Gordon model plus an additional topological term, accounting for the
existence of zero charge excitations (the fermions or the kinks) in the thermal
bath. This result is the 2D version of the low-energy lagrangian at finite
baryon density.
