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Our professor derived a Minkowski force like this:
[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?
[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?