I should evaluate ##\int d^3 p \ \exp(i \vec{p} \cdot \vec{x}) / \sqrt{|p| + m^2}## over all ##\mathbb{R}^3##. How can I do this in spherical coordinates? Since ##\vec{p}## is a position vector in ##\mathbb{R}^3##, our ##\vec{r}## of the spherical coordinates would be just equal to ##\vec{p}##, correct? (The same would be said of ##\vec{x}##, which we could call an ##\vec{r'}##.)(adsbygoogle = window.adsbygoogle || []).push({});

So the integral above would be re-written as ##\int dp \ d\varphi \ d\theta \ p^2 \exp(i \vec{p} \cdot \vec{x}) / \sqrt{|p| + m^2}##. I suppose that the correct range for our "spherical variables" is ##p \in (-\infty, \infty)## and ##\varphi, \theta \in [0, 2 \pi]##. Now the integral would then become ##4 \pi \int dp \ p^2 \exp(i \vec{p} \cdot \vec{x}) / \sqrt{|p| + m^2}##. How do I evaluate it?

EDIT: I don't need to give the final result, just to evaluate the last integral a little further.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Changing coordinate systems

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**