Generalized Mathisson–Papapetrou–Tulczyjew–Dixon equations

We derive two generalizations of Mathisson-Papapetrou-Tulczyjew-Dixon equations from Casalbuoni-Brink-Schwarz type pseudoclassical Lagrangians Majorana spinors on a Riemann-Cartan spacetime. One has "color" freedom, which makes the motion also be generalization Wong equations. The other is spinor model coupled with Rarita-Schwinger field to preserve supersymmetry. coupling torsion modified due existence field. In both extensions, Tulczyjew condition automatically satisfied.