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 ...

  Electron matrix element in a most simple QFT problem, the e+ e- annihilation

+ 3 like - 0 dislike
321 views

In the beginning of PS book there is this short chapter called Invitation: Pair Production in $e^{+}$ $e^{-}$ Annihilation. The first non-zero term of the transition amplitude is:

$$<\mu^{+}\mu^{-}|H_{I}|\gamma>^{\mu}<\gamma|H_{I}|e^{+}e^{-}>_{\mu}$$

The book says that the four elements $<\gamma|H_{I}|e^{+}e^{-}>_{\mu}$ are $\propto (0,1,i,0)$

The electrons fly parallel to the $x$ axis (does the second coordinate accounts then for the total spin?). Now, my question:

What is that imaginary $i$ that appears in the third place? It is supposed to be a component in the $y$ axis (the collision happens in the $XZ$ plane). And what is the first coordinate ($0$)?

I had undergraduate QM long ago. That $i$ reminds me of things largely forgotten. It might have something to do with the spin of the electron or the polarization of the photon?

asked Jan 27, 2016 in Theoretical Physics by Mephisto (15 points) [ revision history ]
edited Jan 28, 2016 by Mephisto

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$\hbar$ysicsOverfl$\varnothing$w
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
...