von Neumann entropy $S$ by analytic continuation of the zeta function $\zeta_{{\rho'}^{-1}}(s)$ and $S(s)$ to $s=1$. A further generalization is $$S \equiv \frac{1}{\alpha}\frac{d\zeta_{\rho^\alpha}(s)}{ds}\bigg\vert_{s =
{-1}/{\alpha}},$$ with $\rho'$ substituting for $\rho$ when $\alpha < 0$.

Further comments and conclusions
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Our work links the Wigner rotations of spins to the behaviour of Bell States under arbitrary Lorentz transformations. We discussed reduced density matrices for identical particle systems, established the Lorentz invariance of their von Neumann entropies, and suggested an invariant regularization through generalized zeta function. In addition, we worked out the explicit expressions of the infinite-dimensional Hermitian generators in the momentum representation. We hope that the results presented here will help to place Relativistic Quantum Information Science on the surer foundations of quantum field theory which is fully compatible with Lorentz symmetry and causality. It is worth emphasizing that we considered the [*full*]{} reduced density matrix with all the degrees of freedom, including the momentum with the reduction prescription of Section V when we go from ${\ensuremath{\mathbb N}}$ particles to $m < {{\ensuremath{\mathbb N}}}$ particles. This is different from the reduced density matrix used, for instance in Ref.[@peres], in which “reduction" to the spin degree of freedom is applied even to 