We present a treatment of many-body fermionic systems that facilitates an expression of well-known quantities in a series expansion inħ. The ensuing semiclassical result contains, to a leading order of the response function, the classical time correlation function of the observable followed by the Weyl-Wigner series; on top of these terms are the periodic-orbit correction terms. The treatment given here starts from linear response assumption of the many-body theory and in its connection with semiclassical theory, it assumes that the one-body quantal system has a classically chaotic dynamics. Applications of the framework are also discussed.