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
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Yang-Mills theory with discontinuous connection

+ 2 like - 0 dislike
405 views

Suppose I have a local gauge group $g$ that is a $C^0$-function over Minkowski spacetime. This implies that the corresponding gauge connection $A_\mu$ is not continuous, i.e. it can have value infinity. More concrete, an interesting case would be the case where $A_\mu$ can have the following values:

Either zero or $\infty$.

If $A_\mu$ is equal to $\infty$, the Yang-Mills action $S$ vanishes. One can define a boundary of the spacetime manifold (assumed as flat) $\partial M$ that separates the singularity of the connection. Would these assumptions lead to the theory

$\sum_{k_1, \dots, k_n=0}^1  \prod_{i=1}^n (\int \mathcal{D}[All. other. fields]e^{iS})_{k_i}$?

Here, the indices $k_i$ indicate from which points the expression $(\int \mathcal{D}[All. other. fields]e^{iS})_{k_i}$ will be separated. If for point number $i$ the value of $k_i$ is zero than the action is not defined on this region, otherwise it is defined. This would induce a sum over all manifold topologies.

Can such a theory be formulated?

asked Jan 31, 2017 in Theoretical Physics by anonymous [ no revision ]

1 Answer

+ 2 like - 0 dislike

One can indeed make operator insertions in gauge theory which amount to prescribing the singularity of the gauge field near some submanifold. One proceeds as you do by removing a small neighborhood of the submanifold and thinking about it as a boundary condition. One can describe magnetic monopoles this way. Look up 't Hooft operator.

Giving these objects dynamics in any sense is a delicate thing, and usually one needs a UV completion of the theory where these singularities are smoothed. In the case of the monopole these are the 't Hooft-Polyakov monopoles one obtains by including the gauge group U(1) inside of SU(2), where the U(1) loop becomes contractible. Then one imagines there is a Higgs scale below which the monopoles look like singularities in the U(1) gauge field but above which are smooth configurations of an SU(2) gauge field which obtain mass proportional to the Higgs scale.

answered Feb 1, 2017 by Ryan Thorngren (1,925 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:
$\varnothing\hbar$ysicsOverflow
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
...