Timeline for Consistency of transformation of scalar fields with mathematical definition of a representation of Lie algebra and Lie group
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jun 10, 2020 at 23:44 | vote | accept | TheQuantumMan | ||
| Jun 10, 2020 at 23:16 | answer | added | J. Murray | timeline score: 2 | |
| Jun 10, 2020 at 23:14 | comment | added | ACuriousMind♦ | If you look at e.g. Wikipedia's definition of a group representation there is no requirement that the vector space be finite-dimensional. | |
| Jun 10, 2020 at 23:01 | comment | added | TheQuantumMan | @ACuriousMind Yes, I think so. A representation should be an element of the general linear group, so I can't see exactly how a differential operator fits this description, although now I suspect that the answer might be trivial | |
| Jun 10, 2020 at 22:56 | comment | added | ACuriousMind♦ | Alright. So, what exactly is your question? The differential operators $L_{\mu\nu}$ are linear operators upon the vector space of scalar fields. So they constitute an (infinite-dimensional) representation of the Lorentz group. Is your problem that $n$ is not finite here? | |
| Jun 10, 2020 at 22:53 | comment | added | TheQuantumMan | @ACuriousMind Thanks for the comment. It was an error. I edited the question now. | |
| Jun 10, 2020 at 22:53 | history | edited | TheQuantumMan | CC BY-SA 4.0 |
added 194 characters in body
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| Jun 10, 2020 at 22:21 | comment | added | ACuriousMind♦ | "Transformations of scalar fields under a general coordinate transformations are generated by differential operators $L_{\mu\nu}=x_\mu\partial_\nu-x_\nu\partial_\mu$." - what do you mean by this? Where have you heard it? (The claim is wrong: The group of diffeomorphisms ($\cong$ "general coordinate transformation") is in general infinite-dimensional, but the algebra of $L_{\mu\nu}$ is clearly finite-dimensional) | |
| Jun 10, 2020 at 22:15 | history | asked | TheQuantumMan | CC BY-SA 4.0 |