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 features!

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

123 submissions , 104 unreviewed
3,547 questions , 1,198 unanswered
4,552 answers , 19,366 comments
1,470 users with positive rep
411 active unimported users
More ...

Massive excitations in Conformal Quantum Field Theory

+ 4 like - 0 dislike
1358 views

Single particle states in quantum field theory appear as discrete components in the spectrum of the Poincare group's action on the state space (i.e. in the decomposition of the Hilbert space of quantum states into irreducible representations of the Poincare group). Classification of irreducible unitary representations of the Poincare group leads to the notions of mass and spin.

Now, suppose we have a conformal QFT and are doing the same trick with the conformal group. Which irreducible representations do we have?

We still have the massless particles (at least I'm pretty sure we do although I don't immediately see the action of special conformal transformations). However, all representations for a given spin s and any mass m > 0 combine into a single irreducible representation.

What sort of physical object corresponds to this representation? Is it possible to construct a scattering theory for such objects? Is it possible to define unstable objects of this sort?

This post has been migrated from (A51.SE)
asked Dec 2, 2011 in Theoretical Physics by Squark (1,700 points) [ no revision ]
Very very naive question: you say there will be (irreducible) representations with a fixed spin $s$ and any mass $m>0$. Since any mass $m$ introduce a length scale $L\sim \frac 1m$, conformal transformations would transform states of different masses into each other. So you would need a theory of uncountable number of particles with any mass $m>0$? If this is correct, doesn't it (naively) seem to be quit hopeless to construct any consistent quantum field theory of this kind? Has such a theory ever been constructed?

This post has been migrated from (A51.SE)
@Heidar, these states would not be particles. This is because the mass spectrum within each such representation is continuous.

This post has been migrated from (A51.SE)

1 Answer

+ 6 like - 0 dislike

Representation theory of the conformal group is discussed in the canonical reference by Mack. As for physical interpretation of the theory, the construction of asymptotic states and scattering theory does not work in CFT for the reasons you write. Rather, the basic observables are Euclidean correlation functions, and the operators of the theory can be arranged into Hilbert space. This is explained in the classic paper of Mack and Luscher.

This post has been migrated from (A51.SE)
answered Dec 3, 2011 by Moshe (2,375 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).
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
...