Timeline for Yang-Mills Functional and Energy
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 15, 2017 at 22:24 | answer | added | user21574 | timeline score: 4 | |
| Apr 24, 2015 at 15:11 | vote | accept | Jjm | ||
| Mar 8, 2015 at 14:04 | answer | added | Tobias Diez | timeline score: 5 | |
| Mar 7, 2015 at 22:19 | comment | added | Igor Khavkine | A connection is a function, so the analogy is rather direct. More precisely, connections are in 1-1 correspondence with sections of a certain affine bundle. This is spelled out explicitly for the case of the Levi-Civita connection of (pseudo-)Riemannian geometry in the answers to this question. | |
| Mar 6, 2015 at 8:53 | comment | added | Jjm | @IgorKhavkine In this case, how are a function and a connection related? | |
| Mar 5, 2015 at 16:05 | comment | added | Igor Khavkine | The archetypal example of an energy functional is $E(u) = \int |\nabla u|^2$. If $u=u(x,y)$ measures the deviation of a taut membrane from perfect flatness (say by height), then $E(u)$ really does represent the potential energy stored in that particular configuration of the membrane. Many analogies flow naturally from this observation, including to this interpretation of the (euclidean signature!) Yang-Mills Functional. | |
| Mar 5, 2015 at 15:37 | history | asked | Jjm | CC BY-SA 3.0 |