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P-form electrodynamics : ウィキペディア英語版
P-form electrodynamics
In theoretical physics, p-form electrodynamics is a generalization of Maxwell's theory of electromagnetism.
==Ordinary (viz. one-form) Abelian electrodynamics==
We have a one-form A, a gauge symmetry
:\mathbf \rightarrow \mathbf + d\alpha
where α is any arbitrary fixed 0-form and d is the exterior derivative, and a gauge-invariant vector current J with density 1 satisfying the continuity equation
:d
*\mathbf=0
where
* is the Hodge dual.
Alternatively, we may express J as a (''d'' − 1)-closed form, but we do not consider that case here.
F is a gauge invariant 2-form defined as the exterior derivative \mathbf=d\mathbf.
A satisfies the equation of motion
:d
*\mathbf=
*\mathbf
(this equation obviously implies the continuity equation).
This can be derived from the action
:S=\int_M \left(
*\mathbf - \mathbf \wedge
*\mathbf\right )
where M is the spacetime manifold.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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