Consider the following integral $$\int \frac{d^4k}{k^2}$$ It is UV divergent but is it IR finite or IR divergent? The integrand is singular as ##k \rightarrow 0## so this suggest an IR divergence but this is no longer the case if I make a shift of the loop momenta by say ##p_1## and write the same integral as $$\int \frac{d^4k}{(k+p_1)^2}$$(adsbygoogle = window.adsbygoogle || []).push({});

Usually we say an IR divergence can be cured by addition of a mass in the denominator (as then the integrand won't be singular as k goes to 0) but isn't the IR divergence also cured by simply making a lorentz transformation on the momenta (assuming ##p_1^2 \neq 0##) ? I don't understand this result so where is the failure in the reasoning?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Shift of momenta cures IR divergence?

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**