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Scalar propagator for lightlike separation

  1. Oct 15, 2014 #1
    Hello everybody.
    I have a free scalar in two dimensions. I know that its propagator will diverge for lightlike separations, that is t= ±x. I have to find the prefactor for this delta function, and I don't know how to do this.
    How do I see from, for example, [tex] \int \frac{dk}{\sqrt{k^2+m^2}} e^{i k x - i \sqrt{k^2+m^2} t}+e^{i k x + i \sqrt{k^2+m^2} t} [/tex] what I get as a prefactor for my [tex] \delta (t-x) [/tex]?

    Normally when calculating this integral we set either x or t to 0, depending on whether the separation is timelike or spacelike, to then restore Lorentz invariance after the integral is solved. What can I do in the case of lightlike separation?
  2. jcsd
  3. Oct 15, 2014 #2


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    Gold Member

    For some reason I can't see your formulas...
  4. Oct 16, 2014 #3
    Wierd. The latex code for the first formula is
    \int \frac{dk}{\sqrt{k^2+m^2}} e^{i k x - i \sqrt{k^2+m^2} t}+e^{i k x + i \sqrt{k^2+m^2} t}
    and it's just the integral that gives you the propagator in position space.
    the second one is just \delta (t-x)
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