# IR non-renormalizable theory

can be a theory with an infinite number of divergent integrals of the form

$$\int \frac{d^{p}k}{k^{m}}$$

for m=1 , 2 , 3 , 4 ,...... so the theory would be IR non renormalizable and you would need and infinite set of operations to cure all the IR divergences

thanks.

• To add to your comment: UV divergences tell you there's something wrong with way you've set up the path integral $\int e^{iS} d\phi$. IR divergences tell you that you've chosen an observable whose expectation value isn't well-defined in the phase you're studying. – user1504 Oct 28 '13 at 21:25
• Forgot to respond. The (probably canonical) example is 2d massless scalars, where the 2-point function of the basic field is divergent. It doesn't make sense to ask about the expection value of $\phi(x)$ in this theory; there is no such operator. – user1504 Dec 3 '13 at 20:53