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
5,352 answers , 22,786 comments
1,470 users with positive rep
820 active unimported users
More ...

  Time-reversal transformation for two-component bosonic models

+ 4 like - 0 dislike
1949 views

Consider a two-component bosonic model $\mathcal{H}=-t\sum_{i\sigma}{b_{i\sigma}b_{i+1\sigma}^\dagger}+h.c. +\sum_{i\sigma\sigma^\prime}U_{\sigma\sigma^\prime}n_{i\sigma}n_{i\sigma^\prime}$. Here $\sigma,\sigma^\prime$ aretwo the pseudo spin, they can take $\uparrow,\downarrow$. I want to know how to define the time-reversal transformation for such two-component bosonic models. Is the definition same as fermion models?


This post imported from StackExchange Physics at 2015-10-14 17:01 (UTC), posted by SE-user fangniuwawa

asked Aug 26, 2015 in Theoretical Physics by fangniuwawa (65 points) [ revision history ]
edited Oct 14, 2015 by Dilaton
It is probably not the same as for fermion models (where time reversal flips the spin) – why should time reversal change the kind of boson (though if the kinds of bosons are some effective particles like right movers and left movers it probably will). I guess the correct time reversal will be independent time reversal for both boson components (but I can be wrong).

This post imported from StackExchange Physics at 2015-10-14 17:01 (UTC), posted by SE-user Sebastian Riese

1 Answer

+ 3 like - 0 dislike

The analysis of one-particle states spanning a representation of the Lorentz group yields up to a phase convention
$$ \mathcal{T} b(E_p,\vec{p},s) \mathcal{T}^\dagger = (-1)^{1/2-s}b(E_p,-\vec{p},-s)$$

The change in the sign of spin is due to the fundamental relation $\mathcal{T} J \mathcal{T}^\dagger = -J$, so this conclusion holds for any kind of collective angular momentum. If $\sigma$ is some collective angular momentum, then the transformation above will apply, if not, you will have to look into the foundations of your model and derive the time-reversal from the transformation of the constituents.

The other question is, of course, what does $i$ stand for. If it is a position index, then it is untransformed, if some kind of fourier-transform/momentum index, then it has to be reverted (without touching the energy spectrum I assume would be somehow in matrix $U$).

answered Oct 18, 2015 by Void (1,645 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$\hbar$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).
Please complete the anti-spam verification




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

Your rights
...