Timeline for Representation theory of spinors - Understanding how $\mathrm{SO}_3$ acts in particle physics
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Mar 15 at 17:56 | comment | added | Andreas Blass | To add a bit to @MichaelEngelhardt's comment, the two elements of $SU_2$ that correspond to a single element of $SO_3$ differ by just a $\pm$ sign. That's the $\pm$ that you noticed when comparing a $2\pi$-rotation with a $4\pi$ or 0 rotation. | |
| Mar 15 at 15:18 | review | Close votes | |||
| Mar 23 at 3:05 | |||||
| Mar 15 at 14:15 | comment | added | Michael Engelhardt | $SU_2$ is a double cover of $SO_3 $. The algebras are isomorphic, but there are two elements of $SU_2 $ for every one element of $SO_3 $. | |
| Mar 15 at 14:06 | comment | added | Andrea | So, in a sense, $SO_3$ gives rise to the Lie-Algebra of $SU_2$? Thanks for the distinction with the quarks :-) | |
| Mar 15 at 14:01 | history | edited | Andrea | CC BY-SA 4.0 |
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| Mar 15 at 14:00 | comment | added | Michael Engelhardt | Yes, the mathematical structures here are Lie algebras and Lie groups. The exponential map is the usual one, it's just a different convention to write the "$i$" explicitly. By the way, every quark has only 3 colors (red, blue, green), and every antiquark has 3 colors (antired, antiblue, antigreen). These are distinct representations of $SU_3 $. | |
| Mar 15 at 13:58 | history | edited | Andrea | CC BY-SA 4.0 |
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| Mar 15 at 13:54 | history | edited | YCor | CC BY-SA 4.0 |
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| S Mar 15 at 13:41 | review | First questions | |||
| Mar 15 at 14:05 | |||||
| S Mar 15 at 13:41 | history | asked | Andrea | CC BY-SA 4.0 |