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Complex integral coming from a 1loop diagram

  1. Aug 15, 2012 #1
    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:

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

    where [itex]\omega[/itex]
    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. jcsd
  3. Aug 15, 2012 #2


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    Homework Helper

    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.
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