p}}_2)\rangle}}$ is an entangled state. Similarly all the Bell states ${\ensuremath{|B^\mu({\ensuremath{\textbf p}}_1,{\ensuremath{\textbf p}}_2)\rangle}}$ discussed previously have von Neumann entanglement entropy of value $2\ln2$. Moreover, as explained, for any physical system the von Neumann entropy of any of the reduced density matrices in quantum field theory will be [*Lorentz invariant*]{}.

Generalized zeta functions and von Neumann Entropy
--------------------------------------------------

Zeta function regularizations have been employed in quantum field theory as gauge and Lorentz-invariant methods for taming and isolating divergences[@hawking; @critchley]. Here we briefly touch upon its relation to the von Neumann entropy.

The generalized zeta function of an operator can be defined to be $$\zeta_{\hat O}(s) \equiv \sum_n\frac{1}{o_n^s}$$ where $o_n$ are eigenvalues of the operator $\hat O$. There is an interesting relation between generalized zeta function and von Neumann entropy. Recall that a density matrix $\rho$ (or, for this matter, $\rho_m$, a reduced density matrix) has von Neumann entropy $$\label{e:415}
S = -Tr({\rho \ln \rho}) = -\sum_n \lambda_n \ln\lambda_n$$ with $\lambda_n$ being the eigenvalues of $\rho$. Note that in the sum, zero eigenvalues do not pose a problem (by L’Hospital rule $\lambda_n\ln\lambda_n$ has no contribution for zero eigenvalues). However in quantum field theory, without regularization, the entropy can suffer from divergences. For 