Timeline for How to separate an exponential with a Hamiltonian with both momentum and position operators?
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6 events
| when toggle format | what | by | license | comment | |
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| Oct 20, 2015 at 13:28 | comment | added | ACuriousMind♦ | @BastianTreichler: Off the top of my head, it's in Quantum Physics by Glimm and Jaffe. Beware, that's no physics book ;) | |
| Oct 20, 2015 at 13:25 | vote | accept | Bass | ||
| Oct 20, 2015 at 13:25 | comment | added | Bass | OK that's great to know. Just in case you know of a QFT textbook where it's done rigorously, I'd be happy to know, thanks. | |
| Oct 20, 2015 at 13:24 | comment | added | ACuriousMind♦ | @BastianTreichler: That's why I said "usual physicist's derivation". One just leaves out the $\delta t^2$ term before integrating although the limit has not yet been taken. If you want a rigorous derivation of the path integral this whole thing becomes more complicated: You need to continue analytically to Euclidean time and do things with the Wiener measure on the space of continuous paths. | |
| Oct 20, 2015 at 13:20 | comment | added | Bass | Okay, the Zassenhaus formula seems to be a better way to factorize the exponential. However, in the Gaussian integral there would still be this $\mathrm{e}^{-\delta t^2/2[p^2,V(q)]}$ term. How do I know I can do the Gaussian integral with this term? The Gaussian integral "happens" before we let $\delta t$ go to $0$. | |
| Oct 20, 2015 at 13:14 | history | answered | ACuriousMind♦ | CC BY-SA 3.0 |