Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,789 comments
1,470 users with positive rep
820 active unimported users
More ...

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

+ 1 like - 3 dislike
3030 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 (7,730 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar\varnothing$sicsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...