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The electromagnetic field on a spacetime $X$ is mathematically modeled by a circle bundle with connection $\nabla$ on $X$. If the underlying bundle is trivial, or else on local coordinate patches $\mathbb{R}^n \hookrightarrow X$ over which it is so, this connection is equivalently a differential 1-form $A \in \Omega^1(\mathbb{R}^n)$.
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 $\{t,x^1, x^2, x^3\}$, the electromagnetic potential $A$ is naturally expanded into corredinate components, traditionally written as
Here
$\phi$ is the electric potential
$\vec A = [A_1, A_2, A_3]$ is the magnetic potential
(for this choice of coordinates).
Section 5 of
Last revised on May 15, 2014 at 05:27:20. See the history of this page for a list of all contributions to it.