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Integral of angular functions over d-dim solid angle

  1. Nov 18, 2015 #1
    Hello everyone! I have a question about angular integration in arbitrary d dimensions. The interest comes from the need to use dimensional regularization. Suppose I start with a 2-dimensional integral and then I have to move to [itex]d=2-\epsilon[/itex] dimension to regularize my integral. Now, suppose [itex]\theta[/itex] is the polar angle in the original 2 dimensions and now I want to compute the following integrals:

    $$
    \int d\Omega_d\cos\theta ,
    $$
    $$
    \int d\Omega_d\cos^2\theta.
    $$

    What is the result? Can I still say that the first integral is zero? What about the second?

    Thanks a lot!
     
  2. jcsd
  3. Nov 23, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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