Timeline for What are the $U(1)$ representations and their generators?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 4, 2021 at 0:27 | vote | accept | tomdodd4598 | ||
| Dec 4, 2021 at 0:17 | comment | added | tomdodd4598 | Ah, I see now, thanks... $e^{i 2 \pi n}$ is only $1$ for integral $n$, and so the definition of a representation only holds for integral $n$. Very interesting! Right, I think I have one more question to post on this topic before I can feel better about it :P | |
| Dec 4, 2021 at 0:09 | history | edited | ACuriousMind♦ | CC BY-SA 4.0 |
added 8 characters in body
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| Dec 4, 2021 at 0:06 | comment | added | ACuriousMind♦ | @turbodiesel4598 I wrote down an equation that must hold for $\rho_n$ to be a group homomorphism (that I actually had a typo in, corrected now). What happens for non-integral $n$? (Further hint: The l.h.s. is $\rho_n(\mathrm{e}^{\mathrm{i}2\pi}) = \rho_n(1) = 1$) | |
| Dec 3, 2021 at 23:59 | comment | added | tomdodd4598 | I suppose the problem is that I don't see what goes wrong for non-integral $n$. It might be something subtle or just because I don't know enough group/representation theory. | |
| Dec 3, 2021 at 22:42 | history | answered | ACuriousMind♦ | CC BY-SA 4.0 |