  We provide an explicit expression for the modular hamiltonian of the von
Neumann algebras associated to the unit double cone for the (fermionic) quantum
field theories of the 2-component Weyl (helicity 1/2) field, and of the
4-component massless Dirac and Majorana fields. To this end, we represent the
one particle spaces of these theories in terms of solutions of the
corresponding wave equations, and obtain the action of the modular group on
them. As an application, we compute the relative entropy between the vacuum of
the massless Majorana field and one particle states associated to waves with
Cauchy data localized in the spatial unit ball.
