Question: Using the Lorentz transformations of the (mathbf{E}) and (mathbf{B}) fields, show that (mathbf{E} cdot mathbf{B}) is a Lorentz invariant; that is, show that (mathbf{E}^{prime} cdot

Using the Lorentz transformations of the $\mathbf{E}$ and $\mathbf{B}$ fields, show that $\mathbf{E} \cdot \mathbf{B}$ is a Lorentz invariant; that is, show that $\mathbf{E}^{\prime} \cdot \mathbf{B}^{\prime}=\mathbf{E} \cdot \mathbf{B}$.

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