Symmetry Operators and Separation of Variables for Dirac's Equation on   Two-Dimensional Spin Manifolds
  A signature independent formalism is created and utilized to determine the general second-order symmetry operators for Dirac's equation on two-dimensional Lorentzian spin manifolds. The formalism is used to characterize the orthonormal frames and metrics that permit the solution of Dirac's equation by separation of variables in the case where a second-order symmetry operator underlies the separation. Separation of variables in complex variables on two-dimensional Minkowski space is also considered. 
Alberto Carignano, Lorenzo Fatibene, Raymond G. McLenaghan and   Giovanni Rastelli
math-ph math.MP nlin.SI