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
3,928 questions , 1,396 unanswered
4,846 answers , 20,597 comments
1,470 users with positive rep
501 active unimported users
More ...

What type of fields are continuous spin representations?

+ 5 like - 0 dislike
89 views

Continuous spin representations (infinite dimensional representations of the Lorentz group) are pretty rarely discussed, and usually not in that much mathematical details. And usually it is done in a very "physicist" way. The field operators for a CSR is given as $\hat \varphi_{\theta_n}(x)$, a field with a family of continuous index (apparently transforming as a 4-component spinor), that transforms as

$$U(\Lambda)\hat \varphi_{\theta_n}(x) U^{-1}(\Lambda)\rightarrow \hat \varphi_{\Gamma_{mn}(\Lambda)\theta_n}(\Lambda x)$$

With the matrices $\Gamma$ a rep of the Lorentz group, written as

$$\Gamma_{mn}(\Lambda) = (e^{-i\alpha J_3}e^{-i\beta J_2}e^{-i\gamma K_3})_{mn}$$

$J$ and $K$ the usual spin transformation matrix.

What object would the field itself correspond to, though? What kind of fiber would correspond to an infinite (continuous) dimensional manifold transforming as such under the Lorentz group, in the same way that a scalar field corresponds to the line bundle, a vector field to the tangent bundle, etc? It's not any tensor bundle, obviously.

This post imported from StackExchange Physics at 2016-05-31 07:23 (UTC), posted by SE-user Slereah
asked May 12, 2016 in Theoretical Physics by Slereah (475 points) [ no revision ]
retagged May 31, 2016

semi-infinite spacelike strings : See http://arxiv.org/abs/1601.02477​

This post imported from StackExchange Physics at 2016-05-31 07:23 (UTC), posted by SE-user jjcale

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$\hbar$ysi$\varnothing$sOverflow
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
...