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Density-density interaction in Luttinger liquids

  1. Jun 4, 2012 #1
    Hi, i'm reading ad article of Lal et al (junction of several weakly interaction quantum wires: a renormalization group study). It's quite cleare but there are some row i'm not good to understand. Could someone help me to understand how obtain equation (6) from equation (4)? I don't know how to obtain from a double integral in x and y a single integral in x under the assumption of a finite range potential.
     

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  2. jcsd
  3. Jun 9, 2012 #2
    Looks like you could solve it by Fourier transform, and then take only the Fourier components of the potential V(0) and V(2kf) to be nonzero. Then transform it back.
     
  4. Jul 2, 2012 #3
    Agree with OhYoungLions.

    Fourier transformation.

    The variable x in Eq. (6) strictly accords with momentum space。
     
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