Feynman propagator for Klein Gordon field in light and matter

[naima]

Could anyone derive an assertion found in "light and matter, a strange theory"?

Feynman writes in his book that the propagator
of the Klein Gordon photon is proportional to
1/(r² - t²)
Have you ever read the proof?

 

[naima]

I found this
http://www.oberlin.edu/physics/dstyer/StrangeQM/Klein-Gordon.pdf"
Where (12) is what I'd like to get.
I do not understand how I can evaluate it using eq (30).

 

[Physics Monkey]

The form follows from dimensional analysis and relativistic invariance. The main thing that requires some work to figure out is the pole structure i.e. what happens when $$r \rightarrow t$$

$$f(x) = \int \frac{d^4 p}{(2\pi)^4} \frac{e^{i p x}}{p^2}$$ is the integral you want to compute (I have used relativistic notation). By scaling $$x \rightarrow \lambda x$$ and using spacetime rotational invariance you should be able to deduce the required form.

Hope this helps.

 

[naima]

Thanks

Have I to use Wick rotation to get the result?

 

[naima]

By scaling $$x \rightarrow \lambda x$$ and using spacetime rotational invariance you should be able to deduce the required form.
Hope this helps.

Thank you very much, Physics Monkey.
This is exactly what I had missed!