Timeline for Principal bundle approach to general relativity
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 30 at 5:15 | comment | added | Ben Whale | @idontgetoutmuch You don't have an institutional logon? I can guarantee that Geroch does not personally care about finding other less reputable sources. Perhaps you would be interested in the work Alexandra Elbakyan? It's also a 56 year old paper - it is very unlikely to contain anything interesting. | |
| Jan 28 at 17:18 | comment | added | idontgetoutmuch | @BenWhale sadly that reference is behind a pay wall | |
| Dec 11, 2020 at 5:44 | comment | added | Ben Whale | So... just to resurrect an old question. If the manifold is four dimensional then the existence of a spin structure is equivalent to parallelization. So the "local" calculations are enough in this case. aip.scitation.org/doi/10.1063/1.1664507 | |
| Mar 29, 2016 at 23:45 | answer | added | Ben Whale | timeline score: 3 | |
| Feb 25, 2016 at 14:10 | comment | added | Bence Racskó | @WillieWong I have been looking into loop quantum gr literature for some time, since they seem to be the ones doing what you said, but it all seems terribly local for me :/ . Maybe I was looking in the wrong place. I'll edit the question soon, which might clarify things. | |
| Feb 24, 2016 at 19:09 | comment | added | Deane Yang | One nice aspect of the Cartan approach is that the differential forms are both global and canonical. | |
| Feb 24, 2016 at 19:01 | comment | added | Deane Yang | This is most easily done using moving frames and Cartan's formulation of the geometric invariants (e,g., connection and curvature) in terms of differential forms. One usually fixes a local orthonormal frame of tangent vectors and works with the dual 1-forms, this can be reformulated using lifted Maurer-Cartan forms on the principal SO(3,1)-bundle. A paper on the overall approach (no mention of GR) is: Griffiths, P. On Cartan's method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry. Duke Math. J. 41 (1974), 775–814. | |
| Feb 24, 2016 at 16:52 | answer | added | Igor Khavkine | timeline score: 5 | |
| Feb 24, 2016 at 15:38 | comment | added | Willie Wong | That said, I don't pretend to fully understand your question. So maybe someone else will give better ideas. | |
| Feb 24, 2016 at 15:35 | comment | added | Willie Wong | One place to look maybe texts on quantum gravity and quantum GR; one approach there is to take the Yang-Mills analogy seriously and start quantization that way, which would be close to what you are thinking about. (But in terms of the analysis, isn't it the case that a lot of meaningful computations really need fixing a local trivialization, hence reduce to a tetrad formalism?) | |
| Feb 24, 2016 at 11:16 | review | First posts | |||
| Feb 24, 2016 at 11:37 | |||||
| Feb 24, 2016 at 11:11 | history | asked | Bence Racskó | CC BY-SA 3.0 |