Timeline for How to obtain time-ordered density correlation function of free Bosonic system via Wick's theorem?
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| when toggle format | what | by | license | comment | |
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| Aug 30, 2019 at 9:43 | vote | accept | Prongs | ||
| Aug 30, 2019 at 9:43 | answer | added | Prongs | timeline score: 0 | |
| Aug 29, 2019 at 22:53 | comment | added | Prongs | Actually, what is bothering me is that $\vert \Phi_0\rangle$ is not the vacuum state so that $\langle \Phi_0 \vert : (\cdots) : \vert \Phi_0 \rangle$ cannot be simply taken as $0$. But pulling things out from that state gives $\langle vac \vert a\cdots a a(x,t)^\dagger a(x,t) a(0,0)^\dagger a(0,0) a^\dagger \cdots a^\dagger\vert vac\rangle$. And that is too many field operators to contract! | |
| Aug 29, 2019 at 22:38 | comment | added | Prongs | @ArtemAlexandrov Thank you for comment. But I think for a Schrodinger field, $a(x), a^\dagger(x)$ is the same as $\phi(x), \phi^\dagger(x)$. And $\rho(x,t)$ is just $a^\dagger(x) a(x)$. We are not considering a Klein-Gordon field here. | |
| Aug 29, 2019 at 22:04 | comment | added | Artem Alexandrov | If you would like to use Wick theorem, it seems that it is convenient to use field-operators (see field operators of 2nd quantized system) and then find how density-density correlation function can be expressed in terms of fields operators. May be this step is not strictily required but for me it is simpler to work in terms of fields rather then ladder operators. Then, you will have time-ordering average and can use Wick theorem to obtain all the possible contractions of fields operators, this contractions will produce something like $(N/V)^2-G_{0,X}G_{X,0}$ where $G$ is Green function. | |
| Aug 29, 2019 at 21:31 | history | edited | Qmechanic♦ |
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| Aug 29, 2019 at 21:24 | history | edited | Prongs | CC BY-SA 4.0 |
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| Aug 28, 2019 at 1:00 | review | First posts | |||
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| Aug 28, 2019 at 0:57 | history | asked | Prongs | CC BY-SA 4.0 |