  A method is presented for the computation of the one-loop effective action at
finite temperature and density. The method is based on an expansion in the
number of spatial covariant derivatives. It applies to general background field
configurations with arbitrary internal symmetry group and space-time
dependence. Full invariance under small and large gauge transformations is
preserved without assuming stationary or Abelian fields nor fixing the gauge.
The method is applied to the computation of the effective action of spin zero
particles in 2+1 dimensions at finite temperature and density and in presence
of background gauge fields. The calculation is carried out through second order
in the number of spatial covariant derivatives. Some limiting cases are worked
out.
