Timeline for What are unitary representations used for in physics?
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9 events
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| May 29, 2023 at 13:52 | comment | added | Voidt | Conversely, a unitary operator on the Hilbnert space always defines a symmetry operation on the state space (the projective space of rays). And therefore, by looking at Wigner's theorem backwards, searching for unitary representations of groups give us a representation of the symmetry group. This is why we are interested in unitary representations: unitary operators on the Hilbert space correspond to the symmetry transformations of the system, which are elements of the symmetry group and act on the states (rays) through the projective representation of the symmetry group. Am I correct? | |
| May 29, 2023 at 13:45 | comment | added | Voidt | So if I understand correctly, symmetry operations are actually group actions on the projective (ray) space of the Hilbert space and not on the Hilbert space itself. These symmetry operations/group actions form a group associated with the system (the symmetry group), and Wigner's theorem tells us that to each group element (i.e each symmetry operation) acting on the projective space through the group action/projective representation, there is a corresponding/assciated unitary operator acting on the Hilbert space directly. | |
| May 22, 2023 at 13:57 | comment | added | ACuriousMind♦ | @Voidt cf. Wigner's theorem | |
| May 22, 2023 at 13:36 | comment | added | Voidt | Hi @ACuriousMind . I am wondering indeed why we are seeking Unitary representations of certain groups to beginning with? I'd be grateful if you could explain it | |
| Jul 19, 2017 at 20:33 | vote | accept | Oliver Gregory | ||
| Mar 18, 2017 at 19:43 | comment | added | ACuriousMind♦ | I discuss the relevance of unitary representations (projective ones, actually) at length in this Q&A of mine. But it sounds to me you're less concerned about the representations as such but about why we are seeking representations of certain groups to begin with, is that correct? | |
| Mar 18, 2017 at 19:30 | answer | added | ZeroTheHero | timeline score: 1 | |
| Mar 18, 2017 at 19:22 | comment | added | user3257624 | You may want to inform your self about "Wigner's theorem" : en.wikipedia.org/wiki/Wigner%27s_theorem | |
| Mar 18, 2017 at 19:03 | history | asked | Oliver Gregory | CC BY-SA 3.0 |