  Local supersymmetry leads to boundary conditions for fermionic fields in
one-loop quantum cosmology involving the Euclidean normal to the boundary and a
pair of independent spinor fields. This paper studies the corresponding
classical properties, i.e. the classical boundary-value problem and boundary
terms in the variational problem. Interestingly, a link is found with the
classical boundary-value problem when spectral boundary conditions are imposed
on a 3-sphere in the massless case. Moreover, the boundary term in the action
functional is derived.
