- #1

Petar Mali

- 290

- 0

[tex]F_{\mu\nu}=-F_{\nu\mu}[/tex]

[tex]F_{ii}\equiv 0[/tex]

[tex]F_{11}=F_{22}=F_{33}=F_{44}=0[/tex]

where

[tex]A_{\mu}=(-\vec{A},\frac{1}{c}\varphi)[/tex][tex](F_{\mu\nu})=\left(\begin{array}{cccc}

0& -B_z&B_y& -\frac{1}{c}E_x\\

B_z&0&-B_x& -\frac{1}{c}E_y \\

-B_y&B_x&0&-\frac{1}{c}E_z\\

\frac{1}{c}E_x& \frac{1}{c}E_y & \frac{1}{c}E_z & 0\\

\end{array} \right)[/tex][tex]F^{\mu\nu}=g^{\mu\rho}g^{\nu\sigma}F_{\rho\sigma}[/tex][tex](F^{\mu\nu})=\left(\begin{array}{cccc}

0& -B_z&B_y& \frac{1}{c}E_x\\

B_z&0&-B_x& \frac{1}{c}E_y \\

-B_y&B_x&0&\frac{1}{c}E_z\\

-\frac{1}{c}E_x& -\frac{1}{c}E_y & -\frac{1}{c}E_z & 0\\

\end{array} \right)[/tex]

**How do I know that [tex]rotA_{\mu}=\frac{\partial A_{\nu}}{\partial x^{\mu}}-\frac{\partial A_{\mu}}{\partial x^{\nu}}[/tex] is electromagnetic field tensor?**