Using the Lorentz transformations of the (mathbf{E}) and (mathbf{B}) fields, show that (E^{2}-B^{2}) is a Lorentz invariant;
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Using the Lorentz transformations of the \(\mathbf{E}\) and \(\mathbf{B}\) fields, show that \(E^{2}-B^{2}\) is a Lorentz invariant; that is, show that \({E^{\prime}}^{2}-B^{\prime 2}=E^{2}-B^{2}\).
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