Spinning Particles in General Relativity

— We analyze the behavior of a spinning particle in gravity, both from a quantum and a classical point of view. We infer that, since the interaction between the space-time curvature and a spinning test particle is expected, then the main features of such an interaction can get light on which degrees of freedom have physical meaning in a quantum gravity theory with fermions. Finally, the dimensional reduction of Papapetrou equations is performed in a 5-dimensional Kaluza-Klein background and Dixon-Souriau results for the motion of a charged spinning body are obtained. 1. – Quantum features of the interaction between spin and gravity The interaction between gravity and fundamental particles is still an open issue of our knowledge. Even if the final answer to this problem must be given by a quantum formulation for the gravitational field, nevertheless we expect that a good effective description (for energy scales much lower that Planck's one) could come out from the study of particles dynamics living on a curved space-time. But also this is a highly non-trivial task, because, in a classical picture a free moving particle follows geodesics lines, but there are no unambiguous indications for the motion of spinning particles; in fact, in this last case, the classical dynamics must be inferred as classical limit of a relativistic quantum mechanical equation. In this respect, let us consider the Dirac equation on a curved space-time γ µ D µ ψ = 0 D µ ψ = ∂ µ − i 2 ω ab µ Σ ab ψ (1)