  The Bell-CHSH inequality in the vacuum state of a relativistic scalar quantum
field is analyzed. Using Weyl operators built with smeared fields localized in
the Rindler wedges, the Bell-CHSH inequality is expressed in terms of the
Lorentz invariant inner products of test functions. A numerical framework for
these inner products is devised. Causality is also explicitly checked by a
numerical evaluation of the Pauli-Jordan function. Violations of the Bell-CHSH
inequality are reported for different values of the particle mass parameter.
