Gauge invariant derivative expansion of the effective action at finite temperature and density and the scalar field in 2+1 dimensions - art. no. 045016

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 t he number of spatial covariant derivatives. It applies to general backgroun d field configurations with an arbitrary internal symmetry group and space- time dependence. Full invariance under small and large gauge transformation s is preserved without assuming stationary or Abelian fields or 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 a nd in the presence of background gauge fields. The calculation is carried o ut through second order in the number of spatial covariant derivatives. Som e limiting cases are worked out.