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 ...

  In quantum field theory with a mass gap, why do states in the asymptotic future/past turn out to have a Fock space structure?

+ 4 like - 0 dislike
1247 views

In quantum field theory with a mass gap, why do states in the asymptotic future/past turn out to have a Fock space structure? For a free quantum field theory, that's trivial, but why is that the case for interacting theories? In fact, the more one thinks about it, the less clear it becomes. If the quanta of the "fundamental" field is unstable, it doesn't show up in the asymptotic Fock space. If the quanta is confined, it also doesn't show up. If there is a stable bound state, it does show up. If there is a stable solitonic particle, it also shows up.

I am very aware of the LSZ formalism, but that presupposes the existence of an asymptotic Fock space structure as a starting point. Besides, it doesn't handle stable solitons.

This post imported from StackExchange Physics at 2014-08-26 21:34 (UCT), posted by SE-user Lawrence Christos
asked Oct 19, 2012 in Theoretical Physics by Lawrence Christos (20 points) [ no revision ]

1 Answer

+ 4 like - 0 dislike

Asymptotically, particles and bound states in a QFT with mass gap behave as noninteracting particles, as the interaction decays exponentially because of the mass gap. Hence they are described by free fields. The physical S-matrix is between all these asymptotic states, and only these. Thus on the level of the asymptotic states we have particle democracy - elementary, composite and nonlocal (solitonic) particles appear on the same footing.

In particular, soliton states are asymptotically also describes by free fields, though LSZ is not directly applicable. (Textbooks conventionally just treat the case where there are neither bound states nor solitons. This includes Weinberg's QFT treatise; however, he at least acknowledges the problem in somewhat cryptic remarks on p.110 of his Vol. 1.)

If there is no mass gap, the situation is significantly more complicated, because then all asymptotic states describe so-called infraparticles, and asymptotic states are not Fock states but Fock states dressed with coherent states made from the massless particles.

[Edit] On the other hand, unstable particles are visible asympotically only through their decay products, hence are not represented by Fock states. However, in approximate theories neglecting interactions that cause instability, one may regard the unstable particles as asymptotic particles.

Similarly, confined particles are represented asymptotically only through the bound states in which they appear, so they are also not represented by Fock states.

This post imported from StackExchange Physics at 2014-08-26 21:34 (UCT), posted by SE-user Arnold Neumaier
answered Oct 19, 2012 by Arnold Neumaier (15,787 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$\hbar$ys$\varnothing$csOverflow
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
...