Timeline for What is Symplectic Area?
Current License: CC BY-SA 2.5
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Jan 24, 2011 at 23:15 | comment | added | Joseph O'Rourke | Wonderfully informative answer! No apologies necessary; I (and I am sure, others) appreciate the tutorial. :-) | |
Jan 24, 2011 at 22:46 | history | edited | Patrick I-Z | CC BY-SA 2.5 |
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Jan 23, 2011 at 16:58 | history | edited | Patrick I-Z | CC BY-SA 2.5 |
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Jan 23, 2011 at 0:22 | history | edited | Patrick I-Z | CC BY-SA 2.5 |
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Jan 22, 2011 at 17:22 | comment | added | Patrick I-Z | It is related, I am afraid that giving a precise answer to your question could lead us too far :-) But in your simple case if $\omega = dp \wedge dq$ (let's say $q=x$ and $p = \dot x$), ${\bf R}^2$ being simply connected there is no major problem, you can chose once and for all $\lambda = p dq$, a standard choice. Then the action is $$\int_0^{2\pi} p(t)\frac{dq(t)}{dt} dt$$, where $\gamma : t \mapsto (p(t), q(t)$. If you choose another primitive, the difference is the differential of a real function which doesn't contribute to the integral on the loop. | |
Jan 22, 2011 at 16:36 | comment | added | john mangual | Is that primitive known as the "Lagrangian"? (In mechanics sense.) | |
Jan 22, 2011 at 16:25 | history | edited | Patrick I-Z | CC BY-SA 2.5 |
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Jan 22, 2011 at 16:19 | history | answered | Patrick I-Z | CC BY-SA 2.5 |