Квадрат векторного потенциала

Last modified by Alexey Popov on 2019/05/13 15:38

F^{\mu\nu} = \partial^\mu A^\nu - \partial^\nu A^\mu

A_\mu F^{\mu\nu} = A_\mu\partial^\mu A^\nu - A_\mu\partial^\nu A^\mu

A_0 F^{00} = \varphi\frac{\partial \varphi}{\partial t}-\varphi\frac{\partial \varphi}{\partial t}

A_0 F^{01} = \varphi\frac{\partial A_x}{\partial t} - \varphi \frac{\partial \rho}{\partial x}

-\varphi\frac{\partial A}{\partial t} - \varphi \nabla \varphi = \varphi E

A_1 F^{00} = A_x\frac{\partial \varphi}{\partial x}-A_x\frac{\partial A_x}{\partial t}

A\nabla \varphi + A \frac{\partial A}{\partial t}

\nabla \cdot (\varphi A) - \varphi (\nabla \cdot A) + \frac{1}{2}\frac{\partial A \cdot A}{\partial t} = 0

\nabla \cdot (\varphi A) + \frac{1}{2}\frac{\varphi \varphi}{\partial t} + \frac{1}{2}\frac{\partial A \cdot A}{\partial t} = 0

\nabla \cdot A = -\frac{1}{2}\frac{1}{\varphi}\frac{\partial A \cdot A}{\partial t}

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Created by Alexey Popov on 2019/05/13 15:38