Timeline for Field theory: equivalence between Hamiltonian and Lagrangian formulation
Current License: CC BY-SA 3.0
12 events
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| Dec 6, 2015 at 22:33 | comment | added | AccidentalFourierTransform | @Mr.T I edited my answer to include a proof of that statement. PS: IMHO you should change the title of your post into something like "Field theory: equivalence between Hamiltonian and Lagrangian formulation" as this is really the topic of your question. This way, it will be useful for other people if they run into the same doubts as you. | |
| Dec 6, 2015 at 22:25 | history | edited | AccidentalFourierTransform | CC BY-SA 3.0 |
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| Dec 6, 2015 at 21:13 | comment | added | anonymous67 | Why $\dot\pi-\partial_i\left(\frac{\partial \mathscr H}{\partial\phi_{,i}}\right)+\frac{\partial \mathscr H}{\partial \phi}=\dot\pi+\frac{\delta H}{\delta \phi}$? | |
| Dec 6, 2015 at 20:43 | vote | accept | anonymous67 | ||
| Dec 6, 2015 at 20:43 | comment | added | anonymous67 | I have found a similar post physics.stackexchange.com/q/134619 Thank you for your help. I will give u the credit of this answer! | |
| Dec 6, 2015 at 20:38 | comment | added | AccidentalFourierTransform | @Mr.T 1) yes: you need the integral sign. 2) If $F(x)$ is any (well-behaved) function (such as $\phi(x)$, $\pi(x)$, or any other function), you can define the functional $F[f]=\int \mathrm dx\ F(x) f(x)$, for any well-behaved function $f(x)$. Therefore, you can have $\pi[f]=\int \mathrm dx\ \pi(x)f(x)$, but Im not sure the use of it (why would you define such a functional? what do you need it for?). | |
| Dec 6, 2015 at 20:33 | comment | added | anonymous67 | Can you show me clearly what are the functionals $\pi$ and $\phi$? (as opposite to the functions $\pi$ and $\phi$) | |
| Dec 6, 2015 at 20:30 | comment | added | anonymous67 | So $$\{A,B\}=\frac{\delta A}{\delta\pi}\frac{\delta B}{\delta\phi}-\frac{\delta A}{\delta\phi}\frac{\delta B}{\delta\pi}$$ is not a good definition? We have to add the integral $\int$? | |
| Dec 6, 2015 at 20:27 | comment | added | AccidentalFourierTransform | @Mr.T I believe it should be more clear now. If you have any other doubt, feel free to ask. | |
| Dec 6, 2015 at 20:23 | history | edited | AccidentalFourierTransform | CC BY-SA 3.0 |
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| Dec 6, 2015 at 20:11 | comment | added | anonymous67 | $$\{H,\pi\}=\frac{\delta H}{\delta\pi}\frac{\delta \pi}{\delta\phi}-\frac{\delta H}{\delta\phi}\frac{\delta \pi}{\delta\pi}$$. What does it mean exactly $\frac{\delta \pi}{\delta\pi}$? Normally I know that $\frac{\delta\pi(a)}{\delta\pi(x)}=\delta(x-a)$ but it seems it is not the same here? | |
| Dec 6, 2015 at 18:59 | history | answered | AccidentalFourierTransform | CC BY-SA 3.0 |