Timeline for Hilbert's sixth problem and QFT description
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 3 at 21:06 | comment | added | Pedro Lauridsen Ribeiro | The perturbative QCD S-matrix (which, as you correctly pointed out, involves an infinite-time limit as well), on its turn, is physically reliable only in the high-energy limit, thanks to asymptotic freedom. | |
| Mar 3 at 21:02 | comment | added | Pedro Lauridsen Ribeiro | The point is what one is able to compute (or prove the existence thereof) for a given QFT model. Lattice QCD calculations assume both finite volume (i.e. infrared) and short-distance (i.e. ultraviolet) cutoffs, so there's no renormalization involved. We do know by the work by Balaban and Magnen, Rivasseau and Sénéor using weak-* compactness sorcery that the continuum limit of pure Yang-Mills Schwinger functions exist for finite volume, but we don't know anything about uniqueness, let alone its thermodynamical limit. For full, matter-coupled QCD we don't even have that. | |
| Mar 3 at 10:51 | comment | added | Peter Kravchuk | Ah, I see. But then you're talking about an order of limits issue. If we take a fixed Schwinger function with fixed arguments, and look at it's perturbative expansion in a fixed scheme, then I do think it will be asymptotic even in QCD. If you ask about more general quantities such as low-energy spectrum, it is indeed a rather special situation to be able to compute them perturbatively. | |
| Mar 3 at 9:00 | vote | accept | XL _At_Here_There | ||
| Mar 3 at 3:09 | comment | added | Pedro Lauridsen Ribeiro | For instance, the perturbative series for quantum chromodynamics in the low-energy regime (e.g. nuclear physics) doesn't seem to be asymptotic at all, due to quark confinement. Color charged states simply don't appear in scattering at that regime. | |
| Mar 3 at 2:20 | comment | added | Peter Kravchuk | What (and what models) do you have in mind when you say that the perturbative series is not asymptotic? (I'm referring to the "not all" parenthetical remark) | |
| Mar 2 at 12:02 | review | Suggested edits | |||
| Mar 2 at 13:41 | |||||
| Mar 2 at 3:50 | vote | accept | XL _At_Here_There | ||
| Mar 3 at 1:50 | |||||
| Mar 2 at 3:39 | history | answered | Pedro Lauridsen Ribeiro | CC BY-SA 4.0 |