Timeline for Physical Interpretation of the Integrand of the Feynman Path Integral
Current License: CC BY-SA 3.0
5 events
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| Sep 16, 2017 at 4:01 | comment | added | Luboš Motl | Dear Bjorn, to get the expansion in terms of Feynman diagrams, you need to analyze the path integral perturbatively, expand it to a power law or Taylor series. You surely can't get the individual terms with different powers of 1/137 - you can't even extract the exponents - by making just an order of magnitude estimate of the whole integral. One point is that every new term in the 1/137 expansion measures a correction to a phase of the previous one. It's mostly phases, and not the absolute values, that are being expanded. $i$ is almost always in the expansion parameter. | |
| Sep 15, 2017 at 9:15 | comment | added | BjornW | Yes that makes sense, thanks. Reason I asked was because I'm trying to show (to myself) how things like a field history with couplings eventually end up in that (1/137)^n lower-probability bin.. It's another thing that's not intuitively clear with the abs mag integrand, but it's not obvious how it appears out of interference either. I guess food for another question :) | |
| Jul 3, 2017 at 16:18 | comment | added | Luboš Motl | Which regions of the path integral you have to resum depends on the precise quantity you're interested in. Only the total sum over all histories has a truly physical meaning. But what was relevant here is that even though the absolute value of the integrand is constant, this property disappears due to interference if you clump the histories into nearby "families". I was meaning families enough to change $S$ by $O(1)$ or so - these families may still be much smaller than ensembles you could use in thermodynamics for other purposes. But they're larger than the minimum from quantum mechanics. | |
| Jul 2, 2017 at 10:32 | comment | added | BjornW | When you write 'coarsegrained histories', do you mean "macroscopically distinct" histories in the thermodynamic sense? So for one such history, the path integral really will sum over a huge number of microscopically distinct histories which then accumulates into a probability amplitude which then can have any magnitude (including complete destructive interference)? | |
| Apr 15, 2013 at 5:46 | history | answered | Luboš Motl | CC BY-SA 3.0 |