Klein-Gordon propagator

  • Thread starter WarnK
  • Start date
  • #1
31
0

Homework Statement


Homework Equations


Show that the KG propagator
[tex] G_F (x) = \int \frac{d^4p}{(2\pi)^4} e^{-ip.x} \frac{1}{p^2-m^2+i\epsilon} [/tex]
satsify
[tex](\square + m^2) G_F (x) = -\delta(x) [/tex]

The Attempt at a Solution


I get
[tex](\square + m^2) G_F (x) = - \int \frac{d^4p}{(2\pi)^4} (p^2-m^2) e^{-ip.x} \frac{1}{p^2-m^2+i\epsilon} [/tex]
but where do I go from there?
 
Last edited:

Answers and Replies

  • #2
pam
455
1
Cancel the numerate and denominator p^2-m^2.
The i epsilon is just a direction how to take the contour, and is negligible here.
The remaining integral is \delta^4.
 
  • #3
malawi_glenn
Science Advisor
Homework Helper
4,786
22
how does (p^2-m^2)/(p^2-m^+i*epsilon) cancel?

I would try to do the limit of epsilon -> 0+
 
Last edited:
  • #4
pam
455
1
how does (p^2-m^2)/(p^2-m^+i*epsilon) cancel?

I would try to do the limit of epsilon -> 0+
That's what
"The i epsilon is just a direction how to take the contour, and is negligible here."
means.
 

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