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”).
Its de Rham differential
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
is the electric potential
is the magnetic potential
(for this choice of coordinates).
Section 5 of
Revised on April 26, 2013 19:14:20
by Urs Schreiber