Our professor derived a Minkowski force like this:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]

F^\mu = \left[ \gamma(e\vec{E} + e(\vec{v}\times \vec{B})) , \gamma \frac{e \vec{E} \vec{v}}{c} \right]

[/itex]

Does this mean that i can write 4-force like this?

[itex]

F^\mu =

\begin{bmatrix}

\gamma(e\vec{E} + e(\vec{v_x}\times \vec{B}))\\

\gamma(e\vec{E} + e(\vec{v_y}\times \vec{B}))\\

\gamma(e\vec{E} + e(\vec{v_z}\times \vec{B}))\\

\gamma \frac{e \vec{E} \vec{v}}{c}

\end{bmatrix}

[/itex]

Short anwser would be ok. How do i put this into a matrix form from which i can get Lorentz matrix ##\Lambda## for boost in $x$ direction?

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# Minkowski force

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