1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dimensional regularization

  1. Aug 14, 2008 #1
    how does dimensional regularization work ?

    i see , how can you calculate integrals in d-dimensions of the form

    [tex] \int d^{d} k F( \vec k ) [/tex] ??

    and for other cases , let us suppose we have the integral

    [tex] \lim_{\varepsilon\rightarrow 0^+}\int \frac{dp}{(2\pi)^{4-\varepsilon}} \frac{2\pi^{(4-\varepsilon)/2}}{\Gamma\left(\frac{4-\varepsilon}{2}\right)} \frac{p^{3-\varepsilon}}{\left(p^2+m^2\right)^1} [/tex]

    there is no way this integral can be calculated
  2. jcsd
  3. Aug 15, 2008 #2


    User Avatar
    Science Advisor

    It works by analytic continuation. Consider the integral

    [tex]\int_0^\infty dx\,{x^n\over x^2+1}.[/tex]

    For [itex]-1<{\rm Re}\,n<1[/itex], the integral converges, and the result is


    We now define this to be the value of the integral for all [itex]n[/itex].
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?