- #1
bnado
- 3
- 0
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?
Thanks
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?
Thanks