The infrared divergence only appears in theories with massless particles (such as photons). They represent a legitimate effect that a complete theory often implies. In fact, in the case of photons, the energy is given by E = h ν ν , where ν ν is the frequency associated to the particle and as it goes to zero, like in the case of soft photons, there will be an infinite number of particles in order to have a finite amount of energy. One way to deal with it is to impose an infrared cutoff and take the limit as the cutoff approaches zero and/or refine the question. Another way is to assign the massless particle a fictitious mass, and then take the limit as the fictitious mass vanishes.