- #1
zetafunction
- 391
- 0
question is why speak about IR (short momentum) and UV (short distances) divergences ?
in fact if we define [tex] \epsilon = 1/\Lambda [/tex]
then both integrals
[tex] \int_{\epsilon}^{\infty}x^{-k}dx [/tex] and the [tex] \int_{0}^{\Lambda}x^{k-2}dx [/tex]
have the same rate of divergence [tex] \Lambda ^{k-1} [/tex] as the regulator 'Lambda' goes to infinity. (simply make a change of variable x=1/t )
then if mathematically is the same to get rid off an UV or an IR divergence , and with a simple change of variable you can turn an IR divergence into an UV one then why make distinction (the logarithmic case is just another question)
in fact if we define [tex] \epsilon = 1/\Lambda [/tex]
then both integrals
[tex] \int_{\epsilon}^{\infty}x^{-k}dx [/tex] and the [tex] \int_{0}^{\Lambda}x^{k-2}dx [/tex]
have the same rate of divergence [tex] \Lambda ^{k-1} [/tex] as the regulator 'Lambda' goes to infinity. (simply make a change of variable x=1/t )
then if mathematically is the same to get rid off an UV or an IR divergence , and with a simple change of variable you can turn an IR divergence into an UV one then why make distinction (the logarithmic case is just another question)