Spin-raising operators and spin-3/2 potentials in quantum cosmology

Local boundary conditions involving field strengths and the normal to the boundary, originally studied in anti-de Sitter spacetime, have been recently considered in one-loop quanhun cosmology. This paper derives the conditions under which 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 caa only be imposed in a flat Euclidean background, for which the gauge freedom in the choice of the potentials remains.