Scalar and spinning particles in an external linearized gravitational wave field

We study the interaction of a scalar and a spinning particle with a coherent lin- earized gravitational wave field treated as a classical spin two external field. The spin degrees of freedom of the spinning particle are described by skew-commuting variables. We derive the explicit expressions for the eigenfunctions and the Green’s functions of the theory. The discussion is exact within the approximation of neglecting radiative corrections and we prove that the result is completely determined by the semi-classical contribution: this is shown by comparing the wave functions with the (pseudo)classical solutions of the Hamilton-Jacobi equation.