Timeline for Representations of the Lorentz group
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 20, 2021 at 18:11 | vote | accept | JustWannaKnow | ||
| Mar 20, 2021 at 18:07 | answer | added | Igor Khavkine | timeline score: 3 | |
| Mar 20, 2021 at 18:00 | history | edited | Igor Khavkine |
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| Mar 20, 2021 at 15:25 | comment | added | gmvh | Fulton & Harris, Representation Theory – A First Course, Springer 2004 (DOI:10.1007/978-1-4612-0979-9) | |
| Mar 20, 2021 at 13:45 | comment | added | JustWannaKnow | @IgorKhavkine my comment applies specially to you, since what you said looks precisely what I'm looking for. | |
| Mar 20, 2021 at 13:44 | comment | added | JustWannaKnow | Hey guys, thanks for the comments! If possible, I'd like some suggestions on these topics you mentioned. I've never studied Lie grous and its representations, I have no idea where to begin. | |
| Mar 20, 2021 at 13:27 | comment | added | gmvh | The formulae you quote are nothing but the physicists' way of expressing the connection between the Lorentz group and its Lie algebra. The mathematically rigorous way of constructing representations of Lie groups from those of the corresponding Lie algebras should be outlined in your preferred textbook on representation theory. | |
| Mar 20, 2021 at 2:42 | comment | added | Igor Khavkine | The discussion around (1)-(3) is a non-rigorous way of recalling that a representation of the Lie algebra can be converted into a representation of the Lie group via the exponential map, and vice versa via differentiation. But it's not hard to find rigorous references for that, if you wish. In (4), the $J$ constitute a representation of the Lorentz Lie algebra as vector fields on $\mathbb{R}^n$, with the bracket is the Lie bracket of vector fields. If you wish, the $J$ are also a representation as linear operators on $V=C^\infty(\mathbb{R}^n)$. | |
| Mar 19, 2021 at 20:10 | review | Close votes | |||
| Mar 21, 2021 at 14:51 | |||||
| Mar 19, 2021 at 20:04 | comment | added | jjcale | See e.g. en.wikipedia.org/wiki/… . | |
| Mar 19, 2021 at 19:12 | history | asked | JustWannaKnow | CC BY-SA 4.0 |