# Checking integration over 4-momentum

1. Oct 3, 2013

### nikol

1. The problem statement, all variables and given/known data
I would like to make sure I am performing the integration correctly. It is a loop integral in QFT:
$\int \frac{d^{4}p}{(2\pi)^{4}}\frac{1}{p^{2}}$
where p is the 4-momentum, Minkowski space.

2. Relevant equations

3. The attempt at a solution
I think you must change to spherical coordinates in which:
$d^{4}p=|p|^{3}sin^{2}\theta sin\phi_{1}d|p|d\theta d\phi_{1}d\phi$
where $|p|=\sqrt{p_{1}^{2}+p_{2}^{2}+p_{3}^{2}-p_{0}^{2}}$
The integration over the 3 angles will give $2\pi^{2}$ and you have to solve now:
$\int \frac{2\pi^{2}p^{3}dp}{(2\pi)^{4}}\frac{1}{p^{2}}=\frac{1}{8\pi^{2}} \int p dp=\frac{p^{2}}{16\pi^{2}}$
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution