Timeline for How can one recover/obtain information from the renormalization group procedure?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| S Nov 23, 2020 at 1:03 | history | bounty ended | CommunityBot | ||
| S Nov 23, 2020 at 1:03 | history | notice removed | CommunityBot | ||
| Nov 16, 2020 at 19:31 | comment | added | JustWannaKnow | @AbdelmalekAbdesselam amazing. I saved the link to read it later because I've been a little busy these past days and I want to read it carefully, and it demands time. I will read it as soon as I can and if something is not clear I reach you back. Anyway, thanks for the comments again, I've been learning so much from you! | |
| Nov 16, 2020 at 19:20 | comment | added | Abdelmalek Abdesselam | @IamWill: Short answer: Yes. However, until you look at the answer in physics.stackexchange I linked to, I am afraid this discussion will not be very productive. One of the main point I make there is the distinction between autonomous vs nonautonomous dynamical systems and the need for an autonomous RG, in order to have a clean notion of "fixed points". You said one ends up with different objects, but it is worse than that: one ends up with objects living in different spaces, and the successive maps are different. | |
| Nov 15, 2020 at 22:27 | comment | added | JustWannaKnow | For completeness, the forementioned answer was this one mathoverflow.net/questions/62770/… | |
| Nov 15, 2020 at 22:26 | comment | added | JustWannaKnow | I've always thought that the difference was explained because you were addressing the continuum limit, whereas the toy model in my post is trying to sketch a more general idea. But now that you mentioned the work of BK, this difference might be explained by the fact that BK were not trying to explain RG, but using an idea. As you mentioned, there is no reescaling at each step and I believe this is another way to say what I mentioned that after each interaction one end up with a different object. I'm getting it right? | |
| Nov 15, 2020 at 22:22 | comment | added | JustWannaKnow | @AbdelmalekAbdesselam your first comment maybe clarifies something it is not very clear to me yet. As you know, I study your answers frequently and in one of them you discuss a more concrete (yet, rather general) model and you proceed to reescale to a unit lattice. There, the initial integral ($Z$ in my post) becomes $Z$ itself but with $V_{0}$ replaced by $RG(V_{0})$. This is a very nice approach, and the ideas are clear to me. In my post, however, after each iteration, one ends up with different object, since at each step the covariance matrix changes $C_{n}\to C_{n+1}$. (Continues) | |
| Nov 15, 2020 at 21:03 | comment | added | Abdelmalek Abdesselam | About (2) vs (1). In statistical mechanics (1), one has a definite starting point $V_0$, say a lattice model at a given temperature and, e.g., zero magnetic field. Then one runs the RG forward from there $V_0\rightarrow V_1\rightarrow V_2\cdots$ and then eventually converge to a fixed point $V_{\ast}$. In QFT or the use of the RG to construct a model in the continuum (2), the story is much more complicated conceptually, let alone technically. See: physics.stackexchange.com/questions/372306/… | |
| Nov 15, 2020 at 20:59 | comment | added | Abdelmalek Abdesselam | It's been a while since I looked the BK article and it is now behind a paywall I can't access, but the intent of the article was not to explain the RG. Rather, they were inspired by the RG and led to the discovery of a new expansion method for infinite volume limits in statistical mechanics, and constructive QFT. As a result, the description in the MO question is not really the RG, because there is no rescaling at each step. This rescaling is important, in order to have the right notion of fixed point. | |
| Nov 15, 2020 at 16:30 | vote | accept | JustWannaKnow | ||
| Nov 15, 2020 at 16:02 | comment | added | JustWannaKnow | Oh, right. This is an important point indeed. But, considering that one such decomposition is chosen, the above scenario is accurate, right? My point is that, usually, it is stated that, because of the above, the problem becomes the study of the RG map I defined in my post. But I was confused on how to recover the initial information once this map is studied. | |
| Nov 15, 2020 at 15:01 | comment | added | Aaron Bergman | RG flow loses information. You can have multiple UV theories that give rise to the same IR fixed point. | |
| Nov 15, 2020 at 14:15 | answer | added | Carlo Beenakker | timeline score: 2 | |
| S Nov 15, 2020 at 0:01 | history | bounty started | JustWannaKnow | ||
| S Nov 15, 2020 at 0:01 | history | notice added | JustWannaKnow | Draw attention | |
| Nov 12, 2020 at 21:41 | history | asked | JustWannaKnow | CC BY-SA 4.0 |