Timeline for Question about the expression for vacuum persistence amplitude $Z[J]$ as a ratio of two Feynman kernels
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 18, 2020 at 12:14 | vote | accept | Solidification | ||
| Jan 17, 2020 at 0:31 | answer | added | Anonjohn | timeline score: 2 | |
| Jan 16, 2020 at 17:45 | comment | added | Solidification | 1) yes. 2) yes. Thanks. Any help would be highly appreciated. I would like to see the exact expression. | |
| Jan 16, 2020 at 17:43 | comment | added | Anonjohn | The heart of the question as it appears to me, IS the imaginary part. I am interpreting the question: 1) where is the vacuum appearing in the RHS. 2) what happened to the boundary conditions? The answer to both these questions lies in the small imaginary part. I would add the imaginary part to the right hand side to get a clear answer. | |
| Jan 16, 2020 at 17:43 | comment | added | Solidification | I don't know if I make sense in my first question. But I think the second one is obviously something I would like to understand. | |
| Jan 16, 2020 at 17:39 | comment | added | Solidification | Yes. You need to add an imaginary part. I just avoided those just to get to the heart of the question. See that the defining expression of $Z$ is $\langle 0,+\infty|0,-\infty\rangle$ which clearly has informations about the vacuum. But if you look at the expression on the RHS, it is not at all clear that the path integral has anything to do with vacuum state. | |
| Jan 16, 2020 at 17:36 | comment | added | Anonjohn | I am not sure this is correct. Atleast without adding a small imaginary part to the hamiltonian to actually project out the vacuum. But what is the question here? | |
| Jan 16, 2020 at 17:34 | history | edited | Solidification | CC BY-SA 4.0 |
added 83 characters in body
|
| Jan 16, 2020 at 17:32 | comment | added | Solidification | @Anonjohn Z[J] is the vacuum persistence amplitude. It is defined as $<0|e^{-iH(t-t^\prime)}|0\rangle$ in the limit $t,t^\prime\to\mp\infty$. Then it can be shown to be equal to the ratio of two Feynman kernels: one in the presence of $J$ and the other in absence of $J$. | |
| Jan 16, 2020 at 17:30 | comment | added | Anonjohn | What is the first question? I am not clear. The quantity $Z[J]$ has a clear interpretation: the transition amplitude from $|q,t\rangle$ to $|q',t'\rangle$ in the presence of an external source $J$ normalized to the same amplitude in the absence of a source. | |
| Jan 16, 2020 at 16:58 | history | edited | Solidification | CC BY-SA 4.0 |
added 14 characters in body
|
| Jan 16, 2020 at 16:42 | history | asked | Solidification | CC BY-SA 4.0 |