  We devise a general setup to investigate the violation of the Bell-CHSH
inequality in the vacuum state in the context of Quantum Field Theory. We test
the method with massless spinor fields in $(1+1)$-dimensional Minkowski
space-time. Alice's and Bob's test functions are explicitly constructed, first
by employing Haar wavelets which are then bumpified into proper test functions
via a smoothening procedure relying on the Planck-taper window function.
Relativistic causality is implemented by requiring the support of Alice's and
Bob's test functions to be located in the left and right Rindler wedges,
respectively. Violations of the Bell-CHSH inequality as close as desired to
Tsirelson's bound are reported. We briefly comment on the extra portal,
compared to earlier works, this opens to scrutinize Bell-CHSH inequalities with
generic, interacting Quantum Field Theories.
