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The electromagnetic field on a spacetime is mathematically modeled by a circle bundle with connection on . If the underlying bundle is trivial, or else on local coordinate patches over which it is so, this connection is equivalently a differential 1-form .
This is then called the electromagnetic potential of the electromagnetic field (sometimes: “vector potential” or “gauge potential of the electromagnetic field”).
is the actual field strength of the electromagnetic field.
On a 4-dimensiona Minkowski spacetime with its canonical coordinates , the electromagnetic potential is naturally expanded into corredinate components, traditionally written as
Here
is the electric potential
is the magnetic potential
(for this choice of coordinates).
The identification of gauge potentials with connections on fiber bundles is due to:
See also at fiber bundles in physics.
History:
A. C. T. Wu, Chen Ning Yang, Evolution of the concept of vector potential in the description of the fundamental interactions, International Journal of Modern Physics A 21 16 (2006) 3235-3277 [doi:10.1142/S0217751X06033143]
Chen Ning Yang, The conceptual origins of Maxwell’s equations and gauge theory, Phyics Today 67 11 (2014) [doi:10.1063/PT.3.2585, pdf]
Review:
Last revised on February 8, 2024 at 10:15:14. See the history of this page for a list of all contributions to it.