Second order symmetry operators for the massive Dirac equation

Abstract Employing the covariant language of two-spinors, we find what conditions a curved four-dimensional Lorentzian spacetime must satisfy for existence second order symmetry operator massive Dirac equation. The are formulated as set Killing spinors satisfying linear differential equations. Using these spinors, then state most general form such an operator. Partial results zeroth and first presented interpreted well. Computer algebra tools from Mathematica package suite xAct were used calculations.