I have a problem understanding the effect of source terms in qft. I am interested in understanding how a static point source will interact with a massless field. Let me consider a simple example of a linear chain of masses coupled by some springs. In the continuum limit, the Lagrangian of that model will only depend on the derivatives of the displacement of the masses and not on the absolute displacements. In qft such a field is called "massless". Now a scalar source term e.g. [tex]\delta(x) \phi(x)[/tex] corresponds to a force acting on one mass point on the chain. Obviously, this will lead to constant acceleration of the system (or of ever growing parts of it). The Hamiltonian will fail to be bounded from below. Apparently, adding a source term leads to a catastrophy. This will happen also for the discrete chain, so it isn't a problem of renormalization. I guess this is what is called an infra-red catastrophy as it involves the excitation of waves of longer and longer wavelength. How is this controlled in qft?