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For massless $\phi^4$ theory, if exterior momentums are going to zero, then this diagram will be

$$\int \frac{dk^4}{k^4}$$ will suffer from infrared divergence. Because the infrared divergence, unlike UV divergence, often has physical meaning, how do I handle this divergence? What's the meaning?

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    $\begingroup$ Check this out: http://arxiv.org/abs/1112.1375. It's a nice introduction. Your problem is discussed. $\endgroup$
    – Steven Mathey
    Commented Aug 19, 2015 at 10:42
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    $\begingroup$ Adding to the article that Steven pointed out. Within dimensional regularization scheme IR divergences are automatically taken into account. You can check that explicitly by dim. reg. computation. Also see Amit's book: amazon.com/Field-Theory-Renormalization-Critical-Phenomena/dp/… IR divergences, if unavoidable, usually means the point about which perturbation theory is constructed is an inappropriate one. $\endgroup$
    – vik
    Commented Sep 3, 2015 at 16:33
  • $\begingroup$ related to physics.stackexchange.com/q/122620 $\endgroup$
    – 346699
    Commented Apr 24, 2017 at 1:36

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