Note on the Path-Integral Variational Approach in the Many-Body Theory

I discuss how a variatonal approach can be extended to systems of identical particles (in particular fermions) within the path-integral treatment. The applicability of the many-body variational principle for path integrals is illustrated for different model systems, and is shown to crucially depend on whether or not a model system possesses the proper symmetry with respect to permutations of identical particles.