We present a novel method to study quantum field theories at finite temperature and density. The method is based on the Haag expansion where the Heisenberg fields of a theory are expanded in a series of normal-ordered asymptotic fields, including the asymptotic fields for bound states. Temperature and chemical potential are introduced simultaneously through the generalized thermal Bogoliubov transformation. We apply this method to the Nambu-Jona-Lasinio model, both in the mean-field approximation and beyond, and show how this example can be extended to study Quantum Chromodynamics at finite temperature and non-zero chemical potential.