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How to show that the Feynman delta function satisfies the inhomogeneous Klein-Gordon equation

+ 1 like - 3 dislike
1400 views

With
$$\Delta_F(x)=\frac1{(2\pi)^4}\int d^4ke^{-ikx}/(k^2-\mu^2+i\epsilon),$$
how can I show that the Feynman delta function satisfies the inhomogeneous [Klein-Gordon equation][1]
$$(\Box +\mu^2)\Delta_F(x)=-\delta^{(4)}(x)?$$

This is problem 3.3 from Mandl & Shaw's QFT text .


  [1]: http://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation

asked Jun 23, 2014 in Theoretical Physics by anonymous [ revision history ]
edited Jun 23, 2014 by Dilaton

Hi, I just saw that you tried to insert a link like it is done on SE. With our editor you can just highlight the text you want to become a link, click on the button that looks like a $\infty$ symbol which opens a popup window where you can insert the URL.

I hope you do not mind that I did with the link to the book what I assumed you wanted to achieve.

I have downvoted, not because it is homework, but because you don't show us what you have tried to far (in other words, you give me the feeling you haven't actually spend any time on the problem). For some hints, see http://physics.stackexchange.com/questions/121524/how-to-show-that-the-feynman-delta-function-satisfies-the-inhomogenous-klein-gor?noredirect=1#comment246395_121524

2 Answers

+ 2 like - 0 dislike

Compute the LHS of your 2nd equation by making use of your 1st equation.

answered Jun 23, 2014 by drake (885 points) [ no revision ]
edited Jun 23, 2014 by drake
+ 1 like - 0 dislike

The answer is "differentiate the expression under the integral sign". The denominator is cancelled, and you get a delta function. I don't know what the confusion is.

answered Jun 24, 2014 by Ron Maimon (7,535 points) [ no revision ]

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