  Local boundary conditions involving field strengths and the normal to the
boundary, originally studied in anti-de Sitter space-time, have been recently
considered in one-loop quantum cosmology. This paper derives the conditions
under which spin-lowering and spin-raising operators preserve these local
boundary conditions on a 3-sphere for fields of spin 0,1/2,1,3/2 and 2.
Moreover, the two-component spinor analysis of the four potentials of the
totally symmetric and independent field strengths for spin 3/2 is applied to
the case of a 3-sphere boundary. It is shown that such boundary conditions can
only be imposed in a flat Euclidean background, for which the gauge freedom in
the choice of the potentials remains. Alternative boundary conditions for
supergravity involving the spinor-valued 1-forms for gravitinos and the normal
to the boundary are also studied.
