Timeline for Infinite dimensional 2-Hilbert spaces
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 15, 2014 at 21:55 | comment | added | Manuel Bärenz | @SamuelMonnier, it just came to my mind, if you were interested in TQFTs, you might search for "non-semisimple" TQFTs and maybe find something useful there? | |
| Sep 15, 2014 at 21:54 | comment | added | Manuel Bärenz | @SamuelMonnier, for any precise definition someone can probably come up with an example where the definition is unsuitable. As for well-studiedness, these guys have already worked out their example in depth a lot (and found some nice insights as I find). I don't know about your example. If you say it's a non-topological theory, then you must assume some background field like a metric. I have only met higher vector spaces in extended TQFTs, so I have no idea how one would use a 2-vector space here. | |
| Sep 15, 2014 at 16:56 | comment | added | Samuel Monnier | For my final question, when I said "field theory", I meant it in the down-to-earth physical sense. Say consider the free boson in dimension 2 or higher. This is a non-topological theory with an infinite dimensional Hilbert space. What kind of object would we associate to codimension 2 manifolds? I would expect the answer to this question to be valid for any reasonable, non-anomalous field theory a physicist could be interested in. | |
| Sep 15, 2014 at 16:51 | comment | added | Samuel Monnier | Thanks... I already have a vague idea along these lines of what a 2-Hilbert space should be, and actually there is even a concrete proposal in the paper by Baez, Baratin, Freidel and Wise. I was asking if there is a precise and well-studied definition people agree upon (the answer seems to be no...). | |
| Sep 12, 2014 at 17:33 | history | answered | Manuel Bärenz | CC BY-SA 3.0 |