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

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

145 submissions , 122 unreviewed
3,930 questions , 1,398 unanswered
4,853 answers , 20,624 comments
1,470 users with positive rep
501 active unimported users
More ...

What is the classification of representations of the d-dimensional Poincare group that can be identified with 'particle representations'?

+ 4 like - 0 dislike
2401 views

What is the classification of representations of the d-dimensional Poincare group that can be identified with 'particle representations'? I am specifically looking for the classification in terms of SU(2) subgroup labels as Srednicki does in chapter 33 of his textbook. 

Edit: Updated to reflect Arnold's clarification.

asked Aug 26, 2014 in Theoretical Physics by DJBunk (80 points) [ revision history ]
edited Aug 28, 2014 by Arnold Neumaier

1 Answer

+ 5 like - 0 dislike

Srednicki assumes in chapter 33 $d=3$ space dimensions. Otherwise (33.11) doesn't make sense. The Lorentz group is in this case a direct product of two $SO(3)$ groups, hence the irreducible representations are labelled by two generalized spin indices, one for each copy of the $SO(3)$. (You can get the latter in terms of a sub $SO(2)$ and corresponding ladder operations.)

However, it is misleading to think of the irreducible representations of the Lorentz group as ''particle representations''. Particles are associated with unitary positive energy representations of the Poincare group, not with arbitrary representations of the Lorentz group.

answered Aug 26, 2014 by Arnold Neumaier (12,365 points) [ revision history ]
edited Aug 28, 2014 by Arnold Neumaier

+1. @Arnold - Thanks for the help clarifying my question and the info. I agree that eqn 33.11 doesn't hold in general. Do you know if it is possible to write down generalized relations and SU(2) labels for arbitrary d dimensions?

For higher $d$ two labels are not enough; for details you'd have to look into a book on group representation theory (perhaps Gilmore or Cornwell). But only the case $d=3$ has a particle interpretation.

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$\hbar$ysics$\varnothing$verflow
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).
To avoid this verification in future, please log in or register.




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

Your rights
...