Timeline for Alternative approaches to topological QFTs
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 12, 2021 at 20:24 | comment | added | Arun Debray | @HollisWilliams There's a nice review article by Rowell-Wang. | |
| Feb 12, 2021 at 11:43 | vote | accept | Hollis Williams | ||
| Feb 12, 2021 at 4:39 | answer | added | user1504 | timeline score: 11 | |
| Feb 11, 2021 at 23:06 | comment | added | Hollis Williams | @ArunDebray That sounds interesting, do you have some reference to start reading about that? | |
| Feb 11, 2021 at 22:54 | comment | added | Arun Debray | @BertramArnold's comment is the answer you're looking for, but there is a physical interpretation of tensor categories in 3d TFT too. 3d topological orders in condensed-matter physics are described in the language of tensor categories: the simple objects correspond to the types of quasiparticles in the theory, the monoidal product corresponds to fusing particles, and more. However, I think this is thought of quite differently than Chern-Simons theory. | |
| Feb 11, 2021 at 15:30 | comment | added | Adrien | As Witten explains in that same paper, this TFT can also be constructed from the WZW model in conformal field theory, which is mathematically rigorous, but maybe that's not what you're looking for. | |
| Feb 11, 2021 at 15:22 | history | edited | Igor Khavkine | CC BY-SA 4.0 |
"The usual" is not correct for the set of all mathematicians.
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| Feb 11, 2021 at 15:14 | comment | added | user1504 | @BertramArnold That really should just be an answer. | |
| Feb 11, 2021 at 14:03 | comment | added | Bertram Arnold | The perturbative approximation to quantum field theory is by now reasonably well understood, references are eg Cattaneo, Reshetikhin and Mnev's "Perturbative quantum gauge theories on manifolds with boundary" (arxiv.org/abs/1507.01221) and Costello and Gwilliam's book "Factorization algebras in quantum field theory" (people.math.umass.edu/~gwilliam/vol2may8.pdf). The former has been used to compute quantum invariants of lens spaces (arxiv.org/abs/1810.06663), the latter to construct a one-loop exact quantization of Chern-Simons theory (arxiv.org/abs/1910.05230). | |
| Feb 11, 2021 at 13:49 | history | edited | YCor | CC BY-SA 4.0 |
added tags
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| Feb 11, 2021 at 13:40 | history | asked | Hollis Williams | CC BY-SA 4.0 |