Improved loop expansion for the effective potential of coupled boson-fermion systems at finite temperature and density

The effective potential $V\left(\phi \right)$ of a scalar field theory coupled to fermions is undefined near $\phi =0\mathrm{}$ if the scalar field has a spontaneously broken symmetry. This shows up in a loop expansion as an imaginary part in $V\left(\phi \right)$ which persists to all temperatures and densities, even when the symmetry is restored. This paper presents a modification of the loop expansion which yields a real $V\left(\phi \right)$ whenever the one-loop fermion corrections restore the symmetry.