Timeline for Tensor Operators
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| Apr 2, 2015 at 18:17 | answer | added | tensorman | timeline score: 7 | |
| Jul 25, 2014 at 1:08 | vote | accept | joshphysics | ||
| May 10, 2014 at 19:21 | answer | added | ZeroTheHero | timeline score: 1 | |
| Oct 14, 2013 at 20:55 | answer | added | Qmechanic♦ | timeline score: 14 | |
| Oct 10, 2013 at 9:11 | answer | added | Frederic Brünner | timeline score: 1 | |
| S Sep 16, 2013 at 7:20 | history | bounty ended | CommunityBot | ||
| S Sep 16, 2013 at 7:20 | history | notice removed | CommunityBot | ||
| Sep 8, 2013 at 12:36 | answer | added | David Bar Moshe | timeline score: 0 | |
| Sep 8, 2013 at 6:57 | answer | added | xuanji | timeline score: 0 | |
| S Sep 8, 2013 at 5:55 | history | bounty started | Manishearth | ||
| S Sep 8, 2013 at 5:55 | history | notice added | Manishearth | Improve details | |
| Aug 9, 2013 at 3:22 | history | edited | joshphysics | CC BY-SA 3.0 |
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| Aug 8, 2013 at 19:12 | comment | added | joshphysics | @Trimok Would you agree that we can define a tensor operator in the way that I did? If so, then it's simply a generalization in which $\rho$ is not restricted to be any representation of $G$. That's kind of the point of the definition I'm trying to make here in fact. I think this generalization is important, because in QFT for example, we might be inclined to consider objects whose indices transform in representations other than some vector representation. | |
| Aug 8, 2013 at 18:59 | comment | added | Trimok | Second chance....But isn't $\rho(g)$ always (if it exists) the fundamental (vectorial) representation of the group $G$ ?. I do not understand your proposal with another representation, while I probably missed some point.... | |
| Aug 8, 2013 at 18:20 | comment | added | Peter Kravchuk | I just want to note that your definition is a bit too high-level, may be. In the sense that what you actually do is: you pick a representation $\rho$, then you 'tensor' it to the representation $\tau$ acting on tensors, and then define an object that is associated to $\tau$ rather than $\rho$. You could as well start with $\tau$. It seems to me that it is also usefull to think of 'linear object valued operators', the elements of $\mathrm{Hom}(\mathcal{H},L\otimes\mathcal{H})=L\otimes\mathrm{Hom}(\mathcal{H},\mathcal{H})$, where $L$ is a vector space acted upon by some representation $\tau$. | |
| Aug 8, 2013 at 17:59 | comment | added | joshphysics | @Trimok Thanks for the comment, but this is not intended to be a question on tensor representations of groups, but rather a question on the notion of a "tensor operator" on a Hilbert space, its formalization, and the existence of existing mathematical literature on such things. | |
| Aug 8, 2013 at 16:42 | history | edited | joshphysics | CC BY-SA 3.0 |
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| Aug 8, 2013 at 7:25 | comment | added | Trimok | For $SU(N)$, there is a direct link with fundamental representations and antisymmetric tensors. Idem for $SO(N)$, (not considering spinorial representations). (Note that they exist duality between these representations thanks to the Levi-Civita symbol) For $SP(N)$, there is a direct link with fundamental representations and symmetric tensors. Of corse, extending to all representations, you may gain correspondence with other tensors. For instance, the adjoint representation represents a mixed tensor $T^i_j$. For SU(N), representation $(20....)$ represents a symmetric traceless tensor. | |
| Aug 8, 2013 at 5:54 | history | tweeted | twitter.com/#!/StackPhysics/status/365350336526950400 | ||
| Aug 8, 2013 at 2:06 | history | asked | joshphysics | CC BY-SA 3.0 |