Timeline for Is $C^{*}$-algebra the most modern way to study QFT?
Current License: CC BY-SA 4.0
15 events
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| Aug 18, 2020 at 18:46 | answer | added | Paul Siegel | timeline score: 8 | |
| Aug 18, 2020 at 15:12 | comment | added | Aaron Bergman | On the other hand, operator algebras do seem to hang around QFT a lot, and just because something hasn’t proved particularly fruitful in the past (algebraic QFT say), it doesn’t mean it won’t be in the future. | |
| Aug 18, 2020 at 15:08 | comment | added | Aaron Bergman | I am (was?) a physicist, so I’d always suggest learning QFT the way the physicists do particularly because it hasn’t been made rigorous. In that sense, you will rarely if ever see a C*-algebra. I don’t think there’s any harm in learning about C*-algebras — they’re pretty cool — but they’re certainly not required and I would not call them the most modern way of looking at things. Cont’d... | |
| Aug 18, 2020 at 14:52 | history | edited | JustWannaKnow | CC BY-SA 4.0 |
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| Aug 18, 2020 at 14:45 | comment | added | JustWannaKnow | I'm gonna add more information to the post. | |
| Aug 18, 2020 at 14:40 | comment | added | JustWannaKnow | I'm approaching this as a mathematician. But I know it's hard to dodge the physics behind it. But I'm really interested in rigorous approaches to both areas. | |
| Aug 18, 2020 at 14:32 | comment | added | Aaron Bergman | Are you approaching this as a mathematician or as a physicist? Are you looking to prove rigorous theorems about stat mech? Do you want to do stat mech like the physicists do? For the latter, I’d say a vanishingly small fraction use C* algebras. | |
| Aug 18, 2020 at 13:59 | answer | added | Mirco A. Mannucci | timeline score: 3 | |
| Aug 18, 2020 at 13:53 | comment | added | JustWannaKnow | In addition, I know people are using $C^{*}$-algebra to study statistical mechanics as well. But I see this as a reflection of the fact that statistical mechanics has some strong connections to QFT. Don't know if this reasoning is accurate, tho. | |
| S Aug 18, 2020 at 13:51 | history | suggested | gmvh | CC BY-SA 4.0 |
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| Aug 18, 2020 at 13:51 | comment | added | JustWannaKnow | And, also, it would be very clarifying to know why people use it, to what kind of problems, the differences between these approaches and so on. | |
| Aug 18, 2020 at 13:49 | comment | added | JustWannaKnow | @AaronBergman I think I am unexperienced enough to say that I don't know yet. My research area is statistical mechanics but QFT ideas end up being important at some level. What level? Still don't know for sure. I think this is one of the points that motivated my question in the first place. I'm having enough trouble trying to learn QFT on my own, and I know some people deal with it by using $C^{*}$-algebra and other tools I've never studied either.... But, on the other hand, I have a background on functional analysis and distribution theory. I wonder if this is enough to some extent. | |
| Aug 18, 2020 at 13:42 | comment | added | Aaron Bergman | Short answer: no. Long answer/clarifying question : what do you want to study QFT for? | |
| Aug 18, 2020 at 13:41 | review | Suggested edits | |||
| S Aug 18, 2020 at 13:51 | |||||
| Aug 18, 2020 at 13:30 | history | asked | JustWannaKnow | CC BY-SA 4.0 |