# Complex integral coming from a 1loop diagram

1. Aug 15, 2012

Hi,
i'm studing the divergent/convergent behavior of some feynman diagrams that emerge from the study of luttinger liquid. One of this diagrams has a loop inside it and loop-integrals has the following form:

$\int_{-\Lambda}^{+\Lambda}dQ\int d\Omega\frac{1}{(\omega-\Omega)-iv(k-Q)}\frac{1}{\Omega-ivQ}$

where $\omega$
and k are total energy and momentum of the incoming fermions and v the Fermi velocity. Could someone help me with the computation of this integral? It would not be hard but i'm blocked. The dQ integral is limited within a window [-L,+L]

2. Aug 15, 2012

### Mute

You can perform a partial fractions decomposition of the term:

$$\frac{1}{\omega-\Omega - i v(k-Q)}\frac{1}{\Omega - ivQ} = \frac{A}{\omega-\Omega - i v(k-Q)} + \frac{B}{\Omega - ivQ}.$$

I found that A and B end up not depending on $\Omega$ or $Q$, but double check that I didn't make an error.