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
4,862 answers , 20,637 comments
1,470 users with positive rep
502 active unimported users
More ...

an Abelian complex statistical phase from exchanging non-Abelian anyons?

+ 3 like - 0 dislike
19 views

We have some discussions in Phys.SE. about the braiding statistics of anyons from a Non-Abelian Chern-Simon theory, or non-Abelian anyons in general.

May I ask: under what (physical or mathematical) conditions, when we exchange non-Abelian anyons in 2+1D, or full winding a non-Abelian anyon to another sets of non-Abelian anyons of a system, the full wave function of the system only obtain a complex phase, i.e. only $\exp[i\theta]$ gained (instead of a braiding matrix)?

Your answer on the conditions can be freely formulated in either physical or mathematical statements. This may be a pretty silly question, but I wonder whether this conditions have any significant meaning... Could this have anyon-basis dependence or anyon-basis independence. Or is there a subset or subgroup or sub-category concept inside the full sets of anyons implied by the conditions.

This post imported from StackExchange Physics at 2014-06-04 11:39 (UCT), posted by SE-user Idear
asked Dec 15, 2013 in Theoretical Physics by wonderich (1,400 points) [ no revision ]

1 Answer

+ 3 like - 0 dislike

If you put a non-Abelian anyon and its anti particle on a sphere, then moving the non-Abelian anyon around its anti particle only induces an Abelian phase.

Also, twisting a non-Abelian anyon by 360$^\circ$ only induces an Abelian phase as well, which define the (fractional) spin of the non-Abelian anyon.

This post imported from StackExchange Physics at 2014-06-04 11:39 (UCT), posted by SE-user Xiao-Gang Wen
answered Jan 22, 2014 by Xiao-Gang Wen (3,319 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$\hbar$ysicsOverf$\varnothing$ow
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
...