Lagrangian formulation of a spinning test particle in a curved space-time with torsion

A consistent Lagrangian approach for the motion of a charged spinning test particle with anomalous magnetic moment in a curved space-time described by a Riemann-Cartan geometry and in the presence of electromagnetic field is proposed. A necessary and sufficient condition for solving the Cauchy problem for the mechanical momentum and spin tensor of the spinning particle is discussed. The constants of motion associated with existence of Killing vectors are considered. Some interesting consequences of equations of motion are discussed