Tsvelik, Quantum Field Theory in Condensed Matter Physics, Cambridge, 1995

Infrared divergence is more important. Their appearance is always an indication of an incorrectly chosen reference ground state. For example, if electrons in a metal attract, it is wrong to approximate them as free particles; the real ground state is a superconducting condensate of electron pairs. This ground state is orthogonal to the ground state of the non-interacting electron gas and therefore is unreachable by a pertubative expansion. There is no universal recipe for how to choose a correct ground state. Sometimes it is easy (as for ordinary superconductors), sometimes it is not easy at all. In fact, this book is all about the possible consequences of infrared divergences.