Timeline for Reference request for $\phi^{4}_{d}$ theory - where to begin?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Sep 19, 2022 at 6:10 | comment | added | Carlo Beenakker | good point, thanks. | |
| Sep 18, 2022 at 23:45 | comment | added | Abdelmalek Abdesselam | @CarloBeenakker Sorry I was not precise: I was asking about the meaning of "requires" or "needs to be". To get started one indeed needs both UV and IR/volume regularizations, but then one can remove both of them in the case of $\phi_3^4$. | |
| Sep 18, 2022 at 19:11 | comment | added | Carlo Beenakker | @AbdelmalekAbdesselam --- I meant to say that the $\phi^4_3$ theory needs to be regularized by cutoff's on both long and short length scales. | |
| Sep 18, 2022 at 17:05 | comment | added | Abdelmalek Abdesselam | @CarloBeenakker: I didn't understand what you meant by $\phi_3^4$ requiring finite volume and ultraviolet cutoff. Could you elaborate. | |
| Aug 24, 2022 at 1:04 | history | bounty ended | CommunityBot | ||
| Aug 17, 2022 at 5:53 | comment | added | Carlo Beenakker | the fermionic counterpart, in $d=2$, is described in Continuous constructive fermionic renormalization | |
| Aug 16, 2022 at 19:54 | comment | added | MathMath | Carlo, do you have suggestions for fermionic models too? You mentioned in your post the bosonic case because I asked about thr bosonic case, but it got me thinking about the fermionic case too. | |
| Aug 16, 2022 at 14:05 | vote | accept | MathMath | ||
| Aug 16, 2022 at 13:24 | comment | added | Carlo Beenakker | $\phi_3^4$ requires both a finite volume and an ultraviolet cutoff. | |
| Aug 16, 2022 at 13:21 | comment | added | MathMath | E.g. this post: mathoverflow.net/questions/383167/… It discusses Nelson's construction of $\phi^{4}_{2}$ and also some questions about $\phi^{4}_{3}$. Nelson's construction, according to Hairer, is for finite volume only. It should be easier than both limits, as I understand. But I suppose we have more complete results by now, right? | |
| Aug 16, 2022 at 13:19 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Aug 16, 2022 at 13:19 | comment | added | MathMath | Carlo, another great answer! Thank you. The references will be of much help! I just want to understand a little more about the state of art of the $\phi^{4}$ theories. I have heard that the measures have been constructed for $\phi^{4}_{2}$ and $\phi^{4}_{3}$, but it is not clear to me if these constructions only involve finite volume + continuum limit or both continuum + thermodynamic limit. | |
| Aug 16, 2022 at 13:06 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |