Extending the results in (B.M.) on one dimensional interacting fermions in a periodic potential we study the infrared behaviour of the two points Schwinger function in the filled band case. If the fermions are spinless such behaviour is completely determined and it depends on the ratio between the amplitude of the gap and the strength of the interaction. If the ratio is large the Schwinger function behaviour is similar to the one in the free non interacting case while if it is small the Schwinger function is deeply modified and it depends on two anomaly indices, in terms of which the occupation number discontinuity and the spectral gap are expressed. A heuristic second order analysis of the spinning case is also performed. 1 Dipartimento di Matematica, Universit`a di Roma, 00185 Roma, Italia 2 Dipartimento di Matematica, Universit`a di Tor Vergata, Roma, Italia 1 Introduction and statement of the results The hamiltonian of a system of fermions with spin oe which move in a field \..