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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?

346699
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    Check this out: http://arxiv.org/abs/1112.1375. It's a nice introduction. Your problem is discussed. – Steven Mathey Aug 19 '15 at 10:42
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    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: http://www.amazon.com/Field-Theory-Renormalization-Critical-Phenomena/dp/9812561196

    IR divergences, if unavoidable, usually means the point about which perturbation theory is constructed is an inappropriate one.

     – vik Sep 03 '15 at 16:33
  • related to https://physics.stackexchange.com/q/122620/ – 346699 Apr 24 '17 at 01:36

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