- #1
BWV
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- 1,781
This is more of a math question than a physics one, but following the discussion of the propagator in Zee's book:
-(∂2+m2)D(x-y)=δ(x-y)
he then gets, by taking the Fourier transform of the Dirac delta and dividing through:
D(x-y) = [itex]\int\frac{d^4k}{2π^4} \frac{e^{ik(x-y)}}{k^2-m^2+iε}[/itex]
I get the FT and adding iε to avoid a pole, but not how you take
D(x-y)= -(∂2+m2)-1[itex]\int\frac{d^4k}{2π^4} e^{ik(x-y)}[/itex]
and change the differential operator outside the integral to [itex]1/ (k^2-m^2) [/itex] inside it
-(∂2+m2)D(x-y)=δ(x-y)
he then gets, by taking the Fourier transform of the Dirac delta and dividing through:
D(x-y) = [itex]\int\frac{d^4k}{2π^4} \frac{e^{ik(x-y)}}{k^2-m^2+iε}[/itex]
I get the FT and adding iε to avoid a pole, but not how you take
D(x-y)= -(∂2+m2)-1[itex]\int\frac{d^4k}{2π^4} e^{ik(x-y)}[/itex]
and change the differential operator outside the integral to [itex]1/ (k^2-m^2) [/itex] inside it