The $\lambda \phi^4$ quantum filed theory is the textbook example (which probably cannot be constructed nonperturbatively; I'm purely interested in perturbation theory). However, usually one treats massive case. I suppose that, in the massless case 1PI and Green function should be also well defined at least outside the mass shell (?). The infrared problems should appear on the level of the S-matrix elements and cross sections. The standard way to solve those problems in case of QED is to consider only inclusive cross-section. They are analysed thoroughly in the context of QED in several textbooks.
Firstly, I would like to make sure whether similar (infrared) problems as in QED appear also in $\lambda \phi^4$ theory. Can I find the analysis of these problems in some book or paper? I'm also interested in actual computations which shows how to deal with those problems. I suppose that one has to consider at lease the second order perturbation theory to encounter IR problems. Am I right?
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