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

146 submissions , 123 unreviewed
3,953 questions , 1,403 unanswered
4,889 answers , 20,762 comments
1,470 users with positive rep
507 active unimported users
More ...

Non-perturbative effects: classical or quantum?

+ 3 like - 0 dislike
21 views

Are non-perturbative effects (solitons) classical or quantum effects (corrections) ? (examples ?)

My confusion stems from the fact that, for instance, an instanton is a classical solution of the equations of motion. Why is it said to be a quantum correction then? At which point does $\hbar$ enter the game? (the problem, at least for me, stems from taking always $\hbar = 1$).

This post imported from StackExchange Physics at 2016-09-04 15:25 (UTC), posted by SE-user BLS
asked Dec 29, 2015 in Theoretical Physics by BLS (60 points) [ no revision ]

1 Answer

+ 3 like - 0 dislike

Instantons appear as classical solutions of Yang-Mills equation due to nontrivial topology of nonabelian gauge group. They may play some role in physics because of requirement of finiteness of vacuum energy. When we ask how explicitly instantons affect on physics, we must use quantum description: nontrivial homotopy group of nonabelian symmetry group and requirement of the finiteness of energy imply the statement that there are infinite number of different topological vacua which are labelled by discrete winding number $n$, and the true vacuum of theory is superposition of these vacua, $$ |\text{vac}\rangle \equiv \sum_{n}e^{in\theta}|n\rangle $$ This is exactly quantum approach. Instantons then acquire as quasiclassical amplitude of tunneling between vacua when we include extended field configurations in path integral (this is required by principle of cluster decomposition of S-matrix), $$ \langle n - 1| \hat{S}|n\rangle \neq 0, $$ and the amplitude is exponent with degree $\sim \frac{1}{\hbar}$. That's where $\hbar$ arises.

This post imported from StackExchange Physics at 2016-09-04 15:25 (UTC), posted by SE-user Name YYY
answered Dec 29, 2015 by NAME_XXX (1,020 points) [ no revision ]
Thank you, but what about generic solitons? Can you give me self-contained references where to find everything needed to understand solitons?

This post imported from StackExchange Physics at 2016-09-04 15:25 (UTC), posted by SE-user BLS
@BLS: you may find the brief description of generic solitons in Weinberg's QFT Vol. 2 (the paragraph about extended field configurations).

This post imported from StackExchange Physics at 2016-09-04 15:25 (UTC), posted by SE-user Name YYY
Ok, thank you. Do u know any other specific references on non-perturbative effects?

This post imported from StackExchange Physics at 2016-09-04 15:25 (UTC), posted by SE-user BLS
@BLS : I also may recommend Rubakov book "Classical theory of gauge fields" (you may find there topological configurations theory as well as applications to the Standard model), Zahed and Brown article "The Skyrme model" (in which baryons are explained in terms of topological configurations called skyrmions).

This post imported from StackExchange Physics at 2016-09-04 15:25 (UTC), posted by SE-user Name YYY

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$\hbar$ysicsO$\varnothing$erflow
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
...