Timeline for How to construct Goldstone bosons from a conserved charge?
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| Sep 29, 2022 at 14:04 | comment | added | Cosmas Zachos | It should be, to the extent the current here is linear in the pion field; it's not a deep point: most QFT texts such as Schwarz's, evidently yours, cover it in the review of current algebra manipulations... | |
| Sep 29, 2022 at 13:04 | comment | added | Louis Chou | Thanks for the answer. I have the following derivation: Expand $j_0(x)$ as $$ j_0(x)=\int \frac{d^3k}{(2\pi)^3}f(k)a_{\vec k}^\dagger e^{-\vec k\cdot x}$$ where I didn't write the $a_{\vec k}$ term since they annihilate the vacuum. And using $H\sim\int d^3 k\omega_{\vec k}a_{\vec k}a_{\vec k}^\dagger$ we can arrive at the result. Is my derivation correct? | |
| Sep 28, 2022 at 15:57 | comment | added | Cosmas Zachos | Schwartz, your text whose (28.8) you are quoting, has reviewed all in his preceding section. Note $\pi(p)$ is not the canonical momentum, but, instead, $\phi(p)$, the pion field itself, and $J_0(x)\propto F\partial_0 \phi(x)$, and its commutation with H yields a time derivative, so $\sim F \nabla \cdot \vec {\mathbf J}(x)\sim F\nabla^2 \phi(x)$... | |
| Sep 28, 2022 at 11:08 | history | edited | Frederic Thomas | CC BY-SA 4.0 |
I changed the formulation of the second part of the post in order to make the question more conceptual.
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| Sep 28, 2022 at 10:40 | history | edited | Qmechanic♦ |
edited tags; edited tags
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| Sep 28, 2022 at 9:26 | review | Close votes | |||
| Oct 14, 2022 at 3:02 | |||||
| S Sep 28, 2022 at 8:44 | review | First questions | |||
| Sep 28, 2022 at 9:08 | |||||
| S Sep 28, 2022 at 8:44 | history | asked | Louis Chou | CC BY-SA 4.0 |