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?

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# I Shift of momenta cures IR divergence?

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