Timeline for Large and small gauge transformations
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14 events
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| Jan 15, 2023 at 14:38 | comment | added | Gold | I suggest you see this review on the subject arxiv.org/abs/1703.05448 and also this one arxiv.org/abs/1801.07064, although the second does not talk much about the quantum theory and soft theorems, while it is really the focus of the first. If you want to know the implications on holography then I suggest arxiv.org/abs/2107.02075. | |
| Jan 15, 2023 at 14:34 | comment | added | Gold | Well there are various such transformations in various theories and what the charge means certainly depends on the specific case. In electrodynamics, the conservation of the large gauge charge in the scattering problem means "charge conservation at every angle" and likewise in gravity the conservation of supertranslation charge means "energy conservation at every angle". In the quantum theory conservation of the charges implies in soft theorems, an extremely important result for holography in asymptotically flat spacetimes. | |
| Jan 15, 2023 at 14:29 | comment | added | dennis | @Gold I agree! What do you think the conserved charge for the asymptotic symmetry given by gauge transformations not equal to the identity on spatial infinity is? | |
| Jan 15, 2023 at 14:09 | comment | added | Gold | As far as I'm aware the two concepts of Large Gauge Transformation you present are different and it's just unfortunate that they get the same name. The first refers to asymptotic symmetries, which are local transformations that turn out to be physical because of their behavior at infinity, instead of mere redundancies. For more details on why these exist see my answer here physics.stackexchange.com/questions/719053/…. | |
| Jan 15, 2023 at 11:31 | comment | added | ACuriousMind♦ | There are at least two different things that are sloppily called "large gauge transformations", see this answer of mine | |
| Jan 15, 2023 at 11:10 | history | edited | dennis | CC BY-SA 4.0 |
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| Jan 15, 2023 at 2:41 | comment | added | Guliano | Homotopic to the identity indeed implies continuously connected to the identity. However, large vs small only has to do with its properties at spatial infinity. Taking your example, the fact that it is equal to the identity at the origin makes it indeed continuously connected to the identity, but it is not the identity at spatial infinity. It can happen that both small and large gauge transformations are connected to the identity, but the question is whether that happens at spatial infinity or somewhere else. In that light, I think the second statement from those notes is incomplete. | |
| Jan 14, 2023 at 16:19 | history | edited | dennis | CC BY-SA 4.0 |
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| Jan 14, 2023 at 16:18 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
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| Jan 14, 2023 at 16:17 | history | edited | dennis | CC BY-SA 4.0 |
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| Jan 14, 2023 at 16:16 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
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| Jan 14, 2023 at 16:03 | comment | added | dennis | @JulianDeV. I found the second statement on p23 of classe.cornell.edu/~pt267/files/documents/A_instanton.pdf | |
| Jan 14, 2023 at 15:57 | comment | added | Guliano | Any more information about your second statement? Because in the first definition, for a gauge transformation to go smoothly to the identity at infinity it needs to be continuously connected to the identity as well. It can't suddenly make a discrete jump when considering spatial infinity. So there might be something missing where you found the second statement. | |
| Jan 14, 2023 at 15:30 | history | asked | dennis | CC BY-SA 4.0 |