Timeline for Gauge-theoretic formulation of Maxwell equations
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 9, 2014 at 22:20 | comment | added | David Roberts♦ | @Urs I gather the OP is after a calculation that takes d*F=0 and dF=0 and outputs what a physicist would recognise as Maxwell's equations. | |
| Sep 9, 2014 at 5:59 | comment | added | Urs Schreiber | ...apart from that saying that the EM-field is a U(1)-principal connection is part of mathematical theory building in physics and not something one may derive from first principles. (Well, one may give some general arguments about the need for gauge fields to be modeled in differential cohomology, but I guess that's not what you are after.) | |
| Sep 9, 2014 at 5:58 | comment | added | Urs Schreiber | Could you say what exactly you would want to see proven? There is the original Maxwell's equations from the 1850s not nvolving any principal bundles. Then there is Dirac's charge quantization argument from the 1930s which argues that this needs to be refined to the version where the electromagnetic field is a connection on a principal bundle. What one may derive is that this is the right structure to produce U(1)-valued line holonomies, which are the gauge coupling action functionals of charged particles (electrons). But apart from that... | |
| Sep 9, 2014 at 3:26 | comment | added | Boyu Zhang | Thank you so much for helping! But this paper simply states the result, without giving a proof. It seems that everyone knows the result, but no one bothers to write down the proof... | |
| Sep 9, 2014 at 0:20 | history | answered | Andy Sanders | CC BY-SA 3.0 |