It is common to use the normalization \(u^{(\alpha) \dagger}(\boldsymbol{p}) u^{(\beta)}(\boldsymbol{p})=(E / m) \delta_{\alpha \beta}\) for a massive free Dirac spinor \(u^{(\alpha)}\), where \(E\) is energy, \(m\) is restmass, and \(\alpha\) and \(\beta\) are spinor indices. Show that this spinor normalization is covariant with respect to a change of Lorentz frame. The free fermion will propagate in a plane-wave state. In a particular Lorentz frame, what is the probability of finding the fermion in a box of volume \(V\) ? How does that probability change under a Lorentz transformation?