Renormalizing the strong-coupling expansion for quantum field theory: present status

Two methods are presented. One is to extrapolate the renormalized lattice series into the critical regime and then take the continuum limit. The second is to determine exactly the renormalized continuum strong coupling expansion using instantons for d < 2. We find our extrapolation procedure for obtaining the continuum limit of the renormalized lattice field theory works well in zero and one dimension when compared with the exact instanton results in the limit lambda goes to infinity. We also discuss a second strong coupling expansion for the lattice field theory valid when M02 goes to minus infinity with lambda