Timeline for What is a symplectic form intuitively?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Mar 31, 2010 at 17:14 | comment | added | Charles Siegel | Yeah, we really, honestly and truly do not know which coordinates are position and which are momentum, all we can get is pairs of coordinates, one of which is each. | |
| Mar 31, 2010 at 17:07 | comment | added | Jan Weidner | This is very interesting to me. So like Theo Johnson-Freyd said, in an arbitrary symplectic manifold we don't know which coordinate is momentum and which is position, the symplectic form lets us just find the other, when we already know one. | |
| Mar 31, 2010 at 12:18 | comment | added | Charles Siegel | Not quite. Though given a direction that we want to think of as position, it tells us what the momentum direction is. What it gives us are pairs: given one coordinate, there's a second so that the pair are canonically conjugate, which means that, with respect to each other, they will act like position and momentum, and that they'll ignore the "other direction" (that is, things will Poisson commute) | |
| Mar 31, 2010 at 11:47 | comment | added | Jan Weidner | Okay thanks, let me try to rephrase/expand your answer a bit to see whether I understand it correctly. Say our system discribes the movement of a particle in some space. Then the symplectic form tells us, which direction in the phase space is the "position direction" and which direction is the "moment direction"? | |
| Mar 31, 2010 at 11:25 | history | answered | Charles Siegel | CC BY-SA 2.5 |