- #1
CAF123
Gold Member
- 2,948
- 88
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 $$\int \frac{d^4k}{(k+p_1)^2}$$
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?
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?