  We check the cancellation of the vacuum energy in the Wess-Zumino model at
the two-loop order in the component field formalisms with and without auxiliary
fields. We show that in both cases the vacuum energy is equal to zero. However,
in the formalism where the auxiliary fields are excluded, the vanishing of the
vacuum energy arises due to the cancellation between the potential and kinetic
energies, while in the formalism with the auxiliary fields, both terms vanish
separately.
