Timeline for Understanding of the expressions for vacuum-to-vacuum transition amplitude
Current License: CC BY-SA 4.0
12 events
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| Jan 5, 2020 at 19:48 | history | edited | Solidification | CC BY-SA 4.0 |
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| Jan 5, 2020 at 19:36 | comment | added | Sunyam | @mithunsengupta123 It's a good idea if you can construct coordinate space path integral (for transition amplitudes and partition function and vaccum-vaccum amplitudes etc) starting from Trotter formula, somehow I feel that that can clear up all your questions. | |
| Jan 5, 2020 at 18:43 | answer | added | Nikita | timeline score: 1 | |
| Jan 5, 2020 at 18:42 | comment | added | Solidification | @Sunyam What boundary condition do you suggest here? In the previous answer I wasn't evaluating vacuum to vacuum amplitude but amplitude of going from $|q_i\rangle$ to $|q_f\rangle$. There boundary conditions would be $q(0)=q_i$ and $q_f=q(T)$. But I agree that as a path integral second expression is not meaningful unless we have a boundary condition. But what boundary condition would appear here and how? | |
| Jan 5, 2020 at 18:38 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
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| Jan 5, 2020 at 18:37 | comment | added | Qmechanic♦ | Related: physics.stackexchange.com/q/409907/2451 and links therein. | |
| Jan 5, 2020 at 18:37 | comment | added | Sunyam | If you see answer of Qmechanic for your other recent question. For second expression to make sense (even at Physicists level of rigour), you have to specify what boundary conditions paths satisfy. If you are integrating over all paths without constraints, it just means you are evaluating $\int_{-\infty}^{+\infty}dq_f\int_{-\infty}^{+\infty}dq_i\langle q_f| e_{}^{- i H t}|q_i\rangle$ for whatever purpose you are after. | |
| Jan 5, 2020 at 18:35 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
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| Jan 5, 2020 at 18:26 | comment | added | Solidification | Yes. I am asking how to relate these two expressions of $Z$. | |
| Jan 5, 2020 at 18:25 | history | edited | Solidification | CC BY-SA 4.0 |
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| Jan 5, 2020 at 18:25 | comment | added | Sunyam | Second expression is under specified. It begs to ask what paths you are integrating over. First expression is a special case of the last expression. | |
| Jan 5, 2020 at 18:19 | history | asked | Solidification | CC BY-SA 4.0 |