Planar theory with spin and tensor forces

We develop techniques for summing parquet diagrams for systems with two-body interactions with spin, tensor, and isospin components. For boson systems, we sum the same set of diagrams which have been used to derive the optimized hypernetted-chain variational theory when the force is independent of spin and isospin. The present derivation leads to unique local approximations in each of the six independent channels. Singularities in any of these channels at either low or high density correspond to instabilities of the physical system. In contrast to previous variational approaches, the need for commutator terms does not arise in this limit. We derive an energy functional from which the equations of motion may be obtained by functional differentiation. The equations of motion may be solved by a paired-phonon-analysis method which requires time proportional to the number of channels present. Although the primary emphasis of this theory is to suggest ways of including realistic nuclear forces in fermion theories, we present some model calculations which demonstrate the capabilities of the present approach. (orig.)