Generalized Mathisson–Papapetrou–Tulczyjew–Dixon equations

Abstract

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