電磁ポテンシャル

magnetic vector potential

B=∇×A {\mathbf B} = \nabla \times {\mathbf A}

electric potential

E=−∇ϕ−∂A∂t {\mathbf E} = -\nabla \phi -\frac{ \partial {\mathbf A} }{ \partial t }

Gauge freedom}

A′=A+∇χϕ′=ϕ−∂χ∂t\begin{aligned} {\mathbf A'} & = & {\mathbf A} + \nabla \chi \\ \phi ' & = & \phi - \frac{ \partial \chi }{ \partial t } \\ \end{aligned}

Lorenz gauge condition

∇⋅A+1c2∂ϕ∂t \nabla \cdot {\mathbf A} +\frac{ 1 }{ c^2 } \frac{ \partial \phi }{ \partial t }

Electromagnetic four-potential}

Ai=(ϕc,A) A^i = \left( \frac{ \phi }{ c } , {\mathbf A} \right)

Lorenz gauge condition

∂iAi=0 \partial_i A^i = 0

Maxwell's equations