Timeline for A set of questions on continuous Gaussian Free Fields (GFF)
Current License: CC BY-SA 4.0
14 events
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| Jul 10, 2020 at 13:53 | history | edited | Abdelmalek Abdesselam | CC BY-SA 4.0 |
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| Jul 9, 2020 at 0:36 | history | bounty ended | JustWannaKnow | ||
| Jul 8, 2020 at 19:53 | history | edited | Abdelmalek Abdesselam | CC BY-SA 4.0 |
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| Jul 8, 2020 at 19:18 | history | edited | Abdelmalek Abdesselam | CC BY-SA 4.0 |
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| Jul 8, 2020 at 18:57 | comment | added | Abdelmalek Abdesselam | To take (1) seriously, or what Carlo probably means by starting with a Hamiltonian and a measure with density $e^{-H}$ you need to replace $\mathbb{R}^d$ by a finite set. So you need a lattice with spacing $1/N$ but then the infinite volume lattice must be replaced by a finite box with $L^d$ sites. So you then have two limits to do $L\rightarrow\infty$ with fixed $N$ (the lattice thermodynamic limit of my previous answer), and then the continuum limit already in infinite volume, i.e., $N\rightarrow\infty$ which is what I explained in this answer. | |
| Jul 8, 2020 at 18:55 | comment | added | JustWannaKnow | I mean, once you worked out the details and defined an infinite volume measure from the discretized version of the model, you get that the measure on $\mathcal{S}'(\mathbb{R}^{d})$ defined by $(-\Delta+m^{2})$ is the 'appropriate' infinite volume measure, but then these measures can only be 'interpreted' a posteriori. | |
| Jul 8, 2020 at 18:53 | comment | added | JustWannaKnow | (...) once you induced these infinite volume measures from the discretized model. Is it true, indeed? | |
| Jul 8, 2020 at 18:53 | comment | added | JustWannaKnow | Just a quick question: as I said, I will work the details later but as far as I understood it by reading it quickly, you proceed by taking limits to construct the infinite volume measures. This is something that confuses me a lot: if I want to work directly on $\mathbb{R}^{d}$. I know I can define (by Minlos-Bochner) the Gaussian measure on $\mathcal{S}'(\mathbb{R}^{d})$ with covariance $(-\Delta+m^{2})$, but it is not clear to me that this has to do with my "measure" (\ref{1}) in the first place. My point is: as far as I know, these connections are only possible once you induced (cont) | |
| Jul 8, 2020 at 18:52 | history | edited | Abdelmalek Abdesselam | CC BY-SA 4.0 |
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| Jul 8, 2020 at 18:49 | comment | added | Abdelmalek Abdesselam | Thanks. I don't think accepting the answer does anything with the bounty. | |
| Jul 8, 2020 at 18:47 | comment | added | JustWannaKnow | Thanks again for the answer! I'm in a hurry, so I can't work out the details right now, but as usual this is an exellent/very detailed answer so I already accepted it because the bounty was going to expire in a few hours. | |
| Jul 8, 2020 at 18:43 | vote | accept | JustWannaKnow | ||
| Jul 8, 2020 at 18:38 | history | edited | Abdelmalek Abdesselam | CC BY-SA 4.0 |
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| Jul 8, 2020 at 18:06 | history | answered | Abdelmalek Abdesselam | CC BY-SA 4.0 |