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

171 submissions , 136 unreviewed
4,258 questions , 1,606 unanswered
5,064 answers , 21,511 comments
1,470 users with positive rep
615 active unimported users
More ...

  Can a theory gain symmetries through quantum corrections?

+ 9 like - 0 dislike
15 views

It is well known that not all symmetries are preserved when quantising a theory, as evinced by renormalising composite operators or by other means, which show that quantum corrections may alter a conservation law, such as with the chiral anomaly, or 'parity' anomaly of gauge fields coupled to fermions in odd dimensions.

However is the reverse possible: can a theory after quantisation gain a symmetry? Or if not, can it gain a 'partial symmetry'?

(For example invariance under $x\to x+a$ for any $a$ is translation symmetry, and invariance under $x\to x+2\pi$ would be said to be a partial symmetry. My question concerns whether a theory can gain a full symmetry, or a partial one at least through being quantised.)

This post imported from StackExchange Physics at 2019-01-11 12:59 (UTC), posted by SE-user user2062542
asked Oct 4, 2017 in Theoretical Physics by user2062542 (85 points) [ no revision ]
Most voted comments show all comments
Nice question. In principle, it is technically possible, but the variation of the action should compensate the variation of the measure -- something certainly non-trivial. I'm not sure how it could work while keeping the theory local. It will be interesting to see what others have to say.

This post imported from StackExchange Physics at 2019-01-11 12:59 (UTC), posted by SE-user AccidentalFourierTransform
There is a thing that has been studied in the past which is called "order-by-(quantum)disorder" that seems to be exactly what you are looking for. As far as I remember, it is discussed in the book "quantum field theory in condensed matter theory" by Tsvelik.

This post imported from StackExchange Physics at 2019-01-11 12:59 (UTC), posted by SE-user Fabian
@AccidentalFourierTransform maybe Chern-Simons theory is an ok example (I realize that is not 100% what OP is looking for, but still, tecnhically, it is not classicaly gauge-invariant, but is quantum-mechanically gauge invariant for integer levels $k$).

This post imported from StackExchange Physics at 2019-01-11 12:59 (UTC), posted by SE-user Solenodon Paradoxus
Well, the renormalization group certainly enhances or suppresses a symmetry in the UV or IR, and lots of model-building (Nielsen-Froggat) is predicated on it. Since the RG is predicated on quantization, this might serve as an example. For instance, supersymmetry is enhanced/achieved in the IR.

This post imported from StackExchange Physics at 2019-01-11 12:59 (UTC), posted by SE-user Cosmas Zachos
One example could be Liouville CFT. In the Lagrangian description there is a single coupling constant $b$. Upon quantising the theory one finds a symmetry $b\to 1/b$ which was not manifestly present in the Lagrangian description. However, it's important to bare in mind that there are generally many ways to specify the same QFT, consequently symmetries that may be manifest in one description may not be manifest in another.

This post imported from StackExchange Physics at 2019-01-11 12:59 (UTC), posted by SE-user Tom Bourton
en.m.wikipedia.org/wiki/Accidental_symmetry ... also many forms of enhanced or emergent symmetry

This post imported from StackExchange Physics at 2019-01-11 12:59 (UTC), posted by SE-user Mitchell Porter
See my answer to this question for an example

This post imported from StackExchange Physics at 2019-01-11 12:59 (UTC), posted by SE-user jpm

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$\hbar$ysicsOv$\varnothing$rflow
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
...