Timeline for Mathematical applications of quantum field theory
Current License: CC BY-SA 4.0
30 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 3, 2020 at 14:21 | history | edited | Abdelmalek Abdesselam |
edited tags
|
|
| Apr 3, 2020 at 7:05 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title (the question was bumped anyway)
|
| Dec 19, 2016 at 11:25 | answer | added | Daniel Pomerleano | timeline score: 2 | |
| Dec 19, 2016 at 5:45 | answer | added | Tom Copeland | timeline score: 1 | |
| Nov 27, 2016 at 23:24 | comment | added | Count Iblis | As I suggest in this comment (Count Iblis 2 weeks ago HIGHLIGHTED REPLY) Analysis done properly should involve a formalism that is closely related to how one gets to a field theory starting from a discrete lattice model. Had QFT, and in particular the way it is used in statistical physics been invented in the 19th century, then mathematicians would likely have defined real numbers in a more physical way, the tension with finitism wouldn't exist. | |
| Nov 27, 2016 at 21:27 | comment | added | miss-tery | Perhaps, Is the counter relations of this question mathoverflow.net/questions/254599 partially connected to your question? | |
| Nov 27, 2016 at 3:01 | answer | added | user1504 | timeline score: 25 | |
| Nov 26, 2016 at 16:46 | answer | added | Abdelmalek Abdesselam | timeline score: 25 | |
| Nov 26, 2016 at 12:58 | comment | added | user25309 | @Alex Gavrilov The idea to look at a geometrical object (of arbitrary dimension) through the two dimensional QFT defined by a string propagating on it, lead to insights (e.g. mirror symmetry) about algebraic varieties of arbitrary dimension. It is true that (non-trivial) QFT is a low dimensional story in the sense that the spacetime on which the QFT lives is low dimensional but geometrical objects of arbitrary dimension can be involved in a different way (e.g. as input data for the construction of a low dimensional QFT). | |
| Nov 26, 2016 at 12:36 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| S Nov 26, 2016 at 12:30 | history | suggested | CommunityBot | CC BY-SA 3.0 |
Removes ambiguity, QFT is also used to mean Quantum Fourier Transform
|
| Nov 26, 2016 at 12:12 | review | Suggested edits | |||
| S Nov 26, 2016 at 12:30 | |||||
| Nov 26, 2016 at 9:00 | comment | added | Alex Gavrilov | If you know something that others do not, then you have an advantage, but how much of an advantage, depends. My personal take on this is that if your domain is not low dimensional topology (or ``low dimensional algebraic geometry''), then you are not likely to make any use of the knowledge which comes from QFT. (Although there are some exceptions, such as one pointed out by dvitek.) | |
| Nov 26, 2016 at 8:33 | answer | added | Count Iblis | timeline score: 13 | |
| Nov 26, 2016 at 7:50 | comment | added | jjcale | What means "Mathematical applications" ? Algebraic quantum field theory is mathematics. | |
| Nov 26, 2016 at 7:44 | answer | added | Dac0 | timeline score: 5 | |
| Nov 26, 2016 at 6:07 | comment | added | მამუკა ჯიბლაძე | @zibadawatimmy You could add that the VOA formalism is essential in clarifying many aspects of the moonshine stuff, which is of course pure mathematics. Can't make this an answer as I am next to ignorant in the field, but from what I know the very notion of vertex operator algebra could not be thought of without QFT insight - it is a mathematical formulation of essential ingredients of a field theory. | |
| Nov 26, 2016 at 1:27 | answer | added | dvitek | timeline score: 33 | |
| Nov 25, 2016 at 21:33 | comment | added | zibadawa timmy | Some conjectures in rational conformal field theory (and VOAs) imply (conjecturally) the existence of braided equivalences between representation categories of certain twisted doubles of groups, and a lot of work has been done to exhibit and classify such equivalences. This work itself involves almost no CFT/QFT in any direct fashion, though; it simply provides a motivation for bothering with the idea. I think this may be characteristic of a lot of things: the "physics" of CFT/QFT suggests intriguing research directions which can be investigated independently. | |
| Nov 25, 2016 at 20:39 | comment | added | Alex Degtyarev | @FedericoPoloni I would say that this is one of the current mathematical models of the very fabric of reality :) | |
| Nov 25, 2016 at 20:38 | comment | added | Sarah | (and people have been studying algebraic varieties for hundreds years longer than they have been studying quantum fields. they are simply more basic as mathematical objects). | |
| Nov 25, 2016 at 20:37 | comment | added | Sarah | @FedericoPoloni: I'm just not interested in the "very fabric of reality" (whatever that is). I'm a mathematician, not a physicist. | |
| Nov 25, 2016 at 20:36 | comment | added | Federico Poloni | It's curious that you consider an algebraic variety more concrete than a quantum field. One is a complete abstraction, the other might arguably be considered the very fabric of reality. As a mathematician I understand your point of view, but to a physicist this must look completely backwards. (To avoid misunderstanding: I am not the downvoter.) | |
| Nov 25, 2016 at 20:08 | answer | added | Bilateral | timeline score: 31 | |
| Nov 25, 2016 at 19:53 | answer | added | Dan Piponi | timeline score: 38 | |
| Nov 25, 2016 at 19:49 | comment | added | Sarah | Would the downvoter like to explain why he/she does not like this question? | |
| Nov 25, 2016 at 19:40 | answer | added | Carlo Beenakker | timeline score: 8 | |
| Nov 25, 2016 at 19:33 | history | edited | Sarah | CC BY-SA 3.0 |
added 239 characters in body
|
| Nov 25, 2016 at 19:25 | review | First posts | |||
| Nov 25, 2016 at 20:00 | |||||
| Nov 25, 2016 at 19:23 | history | asked | Sarah | CC BY-SA 3.0 |