GENERAL RELATIVITY AND GRAVITATION, cilt.50, sa.3, 2018 (SCI-Expanded)
We have found two non-trivial massless Dirac and two massive Rarita-Schwinger solutions in plane wave spacetimes. The first order symmetry operator transforming one of the massless Dirac solution to the other is constructed. The only non-vanishing spinor bilinear generated by the standard spinor basis is obtained and algebraic relations between the induced parallel forms are demonstrated. It is also seen that the spin-3/2 norm of the Rarita-Schwinger solutions enforces to themassless sector.